dr hab. Anna Karczewska, prof. UZ

About

RESEARCH INTERESTS

Nonlinear wave equations beyond Korteweg - de Vries equation

Stochastic Volterra equations with perturbations

Semilinear stochastic Volterra equations

PhD promotions

Bartosz Bandrowski, Faculty of Mathematics, Computer Science and Econometrics, January, 25 2014

Łukasz Rutkowski, Faculty of Physics and Astronomy, May, 10 2016

Maciej Szczeciński, Faculty of Mathematics, Computer Science and Econometrics, under preparation

MONOGRAPHS

Karczewska A., "Convolution type stochastic Volterra equations". Lecture Notes in Nonlinear Analysis, Juliusz Schauder Center for Nonlinear Studies, Vol. 10 (2007), 1-101. PDF-file .

Hot topics

Soliton dynamics in the shallow water problem
Stochastic Volterra equations with perturbations

SUBMITTED PAPERS

Karczewska, A., Rozmej, P., "Comment on the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" by M. Fokou, T.C. Kofane, A. Mohamadou and E. Yomba, Eur. Phys. J. Plus, 132, 410 (2017)", (2018).

Karczewska, A., Szczeciński M., "Martingale solution to stochastic Korteveg - de Vries equation driven by Levy noise", (2017).

Karczewska A., Szczeciński M., "Martingale solution to stochastic extended Korteweg - de Vries equation", (2017).

Karczewska A., Szczeciński M., "The existence of mild solution to stochastic extended KdV equation" (2017).

IN PRINT

Karczewska, A., Infeld E., Rowlands G., Rozmej P. , "Exact cnoidal solutions to the extended KdV equation", Acta Physica Polonica A (2018).

Karczewska, A., Rozmej P., "Adiabatic invariants of second order Korteweg - de Vries type equation" (2017). Chapter in: Theory and Computation in Nonlinear Systems, Springer, in print.

PUBLISHED PAPERS

Karczewska, A., Rozmej P., "Exact superposition solutions to KdV2 equation" Advances in Mathematical Physics, vol. 2018, Article ID 5095482, 9 pages, (2018). DOI: 10.1155/2018/5095482.

Karczewska, A., Rozmej P., Infeld E., "Superposition solutions to the extended KdV equation for water surface waves" Nonlinear Dynamics (2017), DOI 10.1007/s11071-017-3931-1.

Karczewska, A., Rowlands G, Rozmej P., Infeld E., "Single soliton solution to the extended KdV equation over uneven depth", European Physical Journal E (2017) 40: 100, DOI 10.1140/epje/i2017-11591-7.

Karczewska A., Rozmej P., Infeld E., Rowlands G., "Adiabatic invariants of the extended KdV equation", Physics Letters A , 382 4(2017), 270-275.
Karczewska A., Rozmej P., Szczeciński M., Boguniewicz B., "Finite element method for stochastic extended KdV equations" Computational Methods in Physics and Technology 22 1(2016), 19-29.
Karczewska A., Szczeciński M., Rozmej P., Boguniewicz B., "Finite element method for extended KdV equations" International Journal of Applied Mathematics and Computer Science 26 3(2016).
Karczewska A., Rozmej P., Infeld E., "Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Doubts about the invariance of energy " Physical Review E 92, 053202 (2015).
Karczewska A., Rozmej P., Rutkowski Ł., "Problems with energy of waves described by Korteweg de Vries equation " Annales Universitatis Mariae Curie-Skłodowska, Sectio AAA Physica, Vol. 70, (2015), 43-56.
Karczewska, A., Bandrowski B., "A series approach to perturbed stochastic Volterra equations of convolution type", Advances in Pure Mathematics 5 (2015), 660-671.
Karczewska A., Rozmej P., Infeld E., "Shallow water soliton dynamics beyond the Korteweg--de Vries equation" Physical Review E 90, 012907 (2014).
Karczewska A., "Stochastic Volterra Equations of Nonscalar Type in Hilbert Space" Journal of Mathematical Sciences 200 4(2014), 441-448.
Karczewska A., Rozmej P., Rutkowski Ł., "A new nonlinear equation in the shallow water wave problem" Physica Scripta 89 5(2014).
Karczewska A, Lizama C. , "Stochastic Volterra equations under perturbations" Electronic Communications in Probability 19 29(2014), 1-14.
Karczewska, A., Bandrowski, B., Rozmej P. , "Numerical solutions to fractional perturbed Volterra equations" Abstract and Applied Analysis 2012 (2012), 1-19.
Karczewska, A., "On difficulties appearing in the study of stochastic Volterra equations " Quantum Probability and White Noise Analysis, World Scientific 27 (2011), 214-226.
Karczewska, A., "Time regularity of solutions to stochastic evolution equations" in: N. Halidas (Ed.) "Stochastic differential equations", Nova Science Publishers, Inc., New York, (2011), 51-66.
Karczewska, A., Bandrowski, B., Rozmej P.,, "Numerical solutions to integral equations equivalent to differential equations with fractional time" International Journal of Applied Mathematics and Computer Science 20 2(2010), 261-269
Karczewska A., Lizama C., "Solutions to stochastic fractional oscillation equations" Applied Mathematical Letters, Vol. 23 (2010) pp 1361-1366.
Karczewska A., Lizama C., "Solutions to stochastic fractional relaxation equations" Physica Scripta T 136 (2009) No: 014030, pp 1-7.
Karczewska A., "Regularity of solutions to stochastic Volterra equations of convolution type". Integral Transforms and Special Functions, 20 3-4 (2009) 171-176.
Karczewska A., Lizama C., "Strong solutions to stochastic Volterra equations". Journal of Mathematical Analysis and Applications 349 2(2009), 301-310. DOI:10.1016/j.jmaa.2008.09.005.
Karczewska A., Lizama C., "Stochastic fractional Volterra equations in Hilbert space". Discrete and Continuous Dynamical Systems, Supplement (2007), 541-550. PDF-file .
Karczewska A., Lizama C., "Stochastic Volterra equations driven by cylindrical Wiener process". Journal of Evolution Equations 7 (2007), 373-386. math.PR/0610241.
Karczewska A., "Properties of convolutions arising in stochastic Volterra equations". International Journal of Contemporary Mathematical Sciences, Vol. 2, No. 21 (2007), 1037-1052. math.PR/0410510.
Karczewska A., Lizama C., "Regularity of solutions to stochastic Volterra equations with infinite delay", Proc. Amer. Math. Soc. 135 (2007), 531-540. math.PR/0503595.
Karczewska A., Rozmej P., "Numerical solutions to integrodifferential equations which interpolate heat and wave equations", Int. J. Diff. Eqns. Appl. 10 (2005), 15-27. math.NA/0508564.
Karczewska A., "Maximal type inequalities for linear stochastic Volterra equations", Int. J. Pure Appl. Math. 24 (2005), 111-121. math.PR/0412496
Karczewska A., "Stochastic Volterra convolution with Lévy process, Int. J. Pure Appl. Math. 18 (2005), no. 1, 109-120. math.PR/0411148.
Karczewska A., "On the limit measure to stochastic Volterra equations", J. Integral Equations Appl. 15, (2003), 59-77.
Karczewska A., "Regularity and continuity of solutions to stochastic evolution equations" in: G. Da Prato i L. Tubaro (Eds.) "Stochastic Partial Differential Equations and Applications", , Marcel Dekker, New York, (2002), 309-323.
Karczewska A., Zabczyk. J., "Regularity of solutions to stochastic Volterra equations", Rend. Math. Acc. Lincei. s. 9, Vol. 11, No.3 (2001), 141-154.
Karczewska A., Zabczyk. J., "A note on stochastic wave equations", in: G. Lumer and L. Weis (Eds.) "Evolution Equations and their Applications in Physical and Life Sciences",, Marcel Dekker, New York-Basel, (2001), 501-511.
Karczewska A., Zabczyk. J., "Stochastic PDE's with fuction-valued solutions", in: Ph. Clement, F. den Hollander, J. van Neerven and B.de Pagter (Eds.) "Infinite-Dimensional Stochastic Analysis", Royal Netherlands Academy of Arts and Sciences, Amsterdam, (2000), 197-216. PDF-file .
Karczewska A., "Statistical solutions to turbulent diffusion", Nonlinear Analysis, 37 (1999), 635-675.
Karczewska A., "Stochastic integral with respect to cylindrical Wiener process", Annales Universitatis Mariae Curie-Skłodowska, Sec. A, Vol. LII.2,9 (1998), 79-93. math.PR/0511512.
Karczewska A., Wędrychowicz S., "Existence of mild solutions for semilinear equation of evolution", Comment. Math. Univ. Carolinae 37, No. 4 (1996), 695-706.
Karczewska A., "Foias statistical solutions for stochastic Navier-Stokes equation", Nonlinear Analysis, Theory, Methods and Applications, Vol. 27, No. 1 (1996), 97-114.
Karczewska A., "Statistical Solutions for Stochastic Burgers Equation", Statistics & Probability Letters 27 (1996), 305-311.
Karczewska A., "Statistical study of stochastic diffusion equation", Universitatis Jagiellonicae Acta Mathematica, Fasc. XXXII (1995), 201-211.

PREPRINTS

Karczewska, A., Rozmej, P., "Comment on the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" by M. Fokou, T.C. Kofane, A. Mohamadou and E. Yomba, Eur. Phys. J. Plus, 132, 410 (2017)", Preprint: arXiv:1804.01940.

Karczewska, A., Rozmej, P., "New exact superposition solutions to KdV2 equation", Preprint: arXiv:1804.02222.

Karczewska, A., Rozmej P., Infeld E., "Superposition solutions to the extended KdV equation for water surface waves", Preprint: arXiv:1708.05975.

Karczewska A., Szczecinski, M., "Martingale solution to stochastic extended Korteweg - de Vries equation", Preprint: arXiv:1708.03909.

Karczewska A., Szczecinski, M., "Existence of mild solution to stochastic extended Korteweg - de Vries equation ", Preprint: arXiv:1708.03907.

Karczewska A., Szczecinski, M., "Martingale solution to stochastic Korteweg - de Vries equation driven by Levy noise", Preprint: arXiv:1708.03902.

Karczewska, A., Infeld E., Rozmej P., Rowlands G., "Exact solitonic and periodic solutions of the extended KdV equation", Preprint: arXiv:1612.03847.

Karczewska, A., Rowlands G, Rozmej P., Infeld E., "Single soliton solution to the extended KdV equation over uneven depth", Preprint:arXiv:1612.05022.

Karczewska A., Szczecinski, M, Rozmej P., Boguniewicz, B."Finite Element Method for Stochastic Extended KdV Equations". Preprint:arXiv:1604.04226

Karczewska, A., Rozmej P., Szczecinski, M, Boguniewicz, B."Finite Element Method for Extended KdV Equations". Preprint:arXiv:1604.04105

Karczewska, A., Rozmej P., Infeld E., Rowlands, G.,"Adiabatic invariants of the extended KdV equation". Preprint: arXiv:1512.01194

Karczewska, A., Rozmej P., Infeld E.,"Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Is energy always an invariant". Preprint: arXiv:1503.09089

Karczewska, A., Rozmej P., Infeld E.,"Shallow water soliton dynamics beyond KdV". Preprint:nlin.PS/1401.4859

Karczewska, A., Rozmej P., Rutkowski Ł.,"New nonlinear equation of KdV-type for a non-flat bottom". Preprint: nlin.PS/1401.4261

Karczewska A.,"Temporal and spatial regularity of solutions to stochastic Volterra equations of convolution type". Preprint: math.PR/1212.1257

Karczewska, A., Bandrowski, B., ,"A series approach to stochastic Volterra equations of convolution time". Preprint: math.PR/1212.1254

Karczewska, A., "On stochastic Volterra equations of nonscalar type in Hilbert space". Preprint: math.PR/0509012.

Karczewska, A., "Maximal type inequalities for linear stochastic Volterra equations". Preprint: math.PR/0412496

Karczewska, A., "Function-valued stochastic convolutions arising in integrodifferential equations". Preprint: math.PR/0412495

Karczewska A., Rozmej, P. "On numerical solutions to stochastic Volterra equations". Preprint: math.PR/0409026.

Last updated: June 11, 2018 by A.Karczewska@wmie.uz.zgora.pl

INSTITUTE OF MATHEMATICS

dr hab. Anna Karczewska, prof. UZ

About

RESEARCH INTERESTS

Nonlinear wave equations beyond Korteweg - de Vries equation

Stochastic Volterra equations with perturbations

Semilinear stochastic Volterra equations

PhD promotions

Bartosz Bandrowski, Faculty of Mathematics, Computer Science and Econometrics, January, 25 2014

Łukasz Rutkowski, Faculty of Physics and Astronomy, May, 10 2016

Maciej Szczeciński, Faculty of Mathematics, Computer Science and Econometrics, under preparation

MONOGRAPHS

Karczewska A., "Convolution type stochastic Volterra equations". Lecture Notes in Nonlinear Analysis, Juliusz Schauder Center for Nonlinear Studies, Vol. 10 (2007), 1-101. PDF-file .

Hot topics

Soliton dynamics in the shallow water problem

Stochastic Volterra equations with perturbations

SUBMITTED PAPERS

Karczewska, A., Rozmej, P., "Comment on the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" by M. Fokou, T.C. Kofane, A. Mohamadou and E. Yomba, Eur. Phys. J. Plus, 132, 410 (2017)", (2018).

Karczewska, A., Szczeciński M., "Martingale solution to stochastic Korteveg - de Vries equation driven by Levy noise", (2017).

Karczewska A., Szczeciński M., "Martingale solution to stochastic extended Korteweg - de Vries equation", (2017).

Karczewska A., Szczeciński M., "The existence of mild solution to stochastic extended KdV equation" (2017).

IN PRINT

Karczewska, A., Infeld E., Rowlands G., Rozmej P. , "Exact cnoidal solutions to the extended KdV equation", Acta Physica Polonica A (2018).

Karczewska, A., Rozmej P., "Adiabatic invariants of second order Korteweg - de Vries type equation" (2017). Chapter in: Theory and Computation in Nonlinear Systems, Springer, in print.

PUBLISHED PAPERS

Karczewska, A., Rozmej P., "Exact superposition solutions to KdV2 equation" Advances in Mathematical Physics, vol. 2018, Article ID 5095482, 9 pages, (2018). DOI: 10.1155/2018/5095482.

Karczewska, A., Rozmej P., Infeld E., "Superposition solutions to the extended KdV equation for water surface waves" Nonlinear Dynamics (2017), DOI 10.1007/s11071-017-3931-1.

Karczewska, A., Rowlands G, Rozmej P., Infeld E., "Single soliton solution to the extended KdV equation over uneven depth", European Physical Journal E (2017) 40: 100, DOI 10.1140/epje/i2017-11591-7.

Karczewska A., Rozmej P., Infeld E., Rowlands G., "Adiabatic invariants of the extended KdV equation", Physics Letters A , 382 4(2017), 270-275.

Karczewska A., Rozmej P., Szczeciński M., Boguniewicz B., "Finite element method for stochastic extended KdV equations" Computational Methods in Physics and Technology 22 1(2016), 19-29.

Karczewska A., Szczeciński M., Rozmej P., Boguniewicz B., "Finite element method for extended KdV equations" International Journal of Applied Mathematics and Computer Science 26 3(2016).

Karczewska A., Rozmej P., Infeld E., "Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Doubts about the invariance of energy " Physical Review E 92, 053202 (2015).

Karczewska A., Rozmej P., Rutkowski Ł., "Problems with energy of waves described by Korteweg de Vries equation " Annales Universitatis Mariae Curie-Skłodowska, Sectio AAA Physica, Vol. 70, (2015), 43-56.

Karczewska, A., Bandrowski B., "A series approach to perturbed stochastic Volterra equations of convolution type", Advances in Pure Mathematics 5 (2015), 660-671.

Karczewska A., Rozmej P., Infeld E., "Shallow water soliton dynamics beyond the Korteweg--de Vries equation" Physical Review E 90, 012907 (2014).

Karczewska A., "Stochastic Volterra Equations of Nonscalar Type in Hilbert Space" Journal of Mathematical Sciences 200 4(2014), 441-448.

Karczewska A., Rozmej P., Rutkowski Ł., "A new nonlinear equation in the shallow water wave problem" Physica Scripta 89 5(2014).

Karczewska A, Lizama C. , "Stochastic Volterra equations under perturbations" Electronic Communications in Probability 19 29(2014), 1-14.

Karczewska, A., Bandrowski, B., Rozmej P. , "Numerical solutions to fractional perturbed Volterra equations" Abstract and Applied Analysis 2012 (2012), 1-19.

Karczewska, A., "On difficulties appearing in the study of stochastic Volterra equations " Quantum Probability and White Noise Analysis, World Scientific 27 (2011), 214-226.

Karczewska, A., "Time regularity of solutions to stochastic evolution equations" in: N. Halidas (Ed.) "Stochastic differential equations", Nova Science Publishers, Inc., New York, (2011), 51-66.

Karczewska, A., Bandrowski, B., Rozmej P.,, "Numerical solutions to integral equations equivalent to differential equations with fractional time" International Journal of Applied Mathematics and Computer Science 20 2(2010), 261-269

Karczewska A., Lizama C., "Solutions to stochastic fractional oscillation equations" Applied Mathematical Letters, Vol. 23 (2010) pp 1361-1366.

Karczewska A., Lizama C., "Solutions to stochastic fractional relaxation equations" Physica Scripta T 136 (2009) No: 014030, pp 1-7.

Karczewska A., "Regularity of solutions to stochastic Volterra equations of convolution type". Integral Transforms and Special Functions, 20 3-4 (2009) 171-176.

Karczewska A., Lizama C., "Strong solutions to stochastic Volterra equations". Journal of Mathematical Analysis and Applications 349 2(2009), 301-310. DOI:10.1016/j.jmaa.2008.09.005.

Karczewska A., Lizama C., "Stochastic fractional Volterra equations in Hilbert space". Discrete and Continuous Dynamical Systems, Supplement (2007), 541-550. PDF-file .

Karczewska A., Lizama C., "Stochastic Volterra equations driven by cylindrical Wiener process". Journal of Evolution Equations 7 (2007), 373-386. math.PR/0610241.

Karczewska A., "Properties of convolutions arising in stochastic Volterra equations". International Journal of Contemporary Mathematical Sciences, Vol. 2, No. 21 (2007), 1037-1052. math.PR/0410510.

Karczewska A., Lizama C., "Regularity of solutions to stochastic Volterra equations with infinite delay", Proc. Amer. Math. Soc. 135 (2007), 531-540. math.PR/0503595.

Karczewska A., Rozmej P., "Numerical solutions to integrodifferential equations which interpolate heat and wave equations", Int. J. Diff. Eqns. Appl. 10 (2005), 15-27. math.NA/0508564.

Karczewska A., "Maximal type inequalities for linear stochastic Volterra equations", Int. J. Pure Appl. Math. 24 (2005), 111-121. math.PR/0412496

Karczewska A., "Stochastic Volterra convolution with Lévy process, Int. J. Pure Appl. Math. 18 (2005), no. 1, 109-120. math.PR/0411148.

Karczewska A., "On the limit measure to stochastic Volterra equations", J. Integral Equations Appl. 15, (2003), 59-77.

Karczewska A., "Regularity and continuity of solutions to stochastic evolution equations" in: G. Da Prato i L. Tubaro (Eds.) "Stochastic Partial Differential Equations and Applications", , Marcel Dekker, New York, (2002), 309-323.

Karczewska A., Zabczyk. J., "Regularity of solutions to stochastic Volterra equations", Rend. Math. Acc. Lincei. s. 9, Vol. 11, No.3 (2001), 141-154.

Karczewska A., Zabczyk. J., "A note on stochastic wave equations", in: G. Lumer and L. Weis (Eds.) "Evolution Equations and their Applications in Physical and Life Sciences",, Marcel Dekker, New York-Basel, (2001), 501-511.

Karczewska A., Zabczyk. J., "Stochastic PDE's with fuction-valued solutions", in: Ph. Clement, F. den Hollander, J. van Neerven and B.de Pagter (Eds.) "Infinite-Dimensional Stochastic Analysis", Royal Netherlands Academy of Arts and Sciences, Amsterdam, (2000), 197-216. PDF-file .

Karczewska A., "Statistical solutions to turbulent diffusion", Nonlinear Analysis, 37 (1999), 635-675.

Karczewska A., "Stochastic integral with respect to cylindrical Wiener process", Annales Universitatis Mariae Curie-Skłodowska, Sec. A, Vol. LII.2,9 (1998), 79-93. math.PR/0511512.

Karczewska A., Wędrychowicz S., "Existence of mild solutions for semilinear equation of evolution", Comment. Math. Univ. Carolinae 37, No. 4 (1996), 695-706.

Karczewska A., "Foias statistical solutions for stochastic Navier-Stokes equation", Nonlinear Analysis, Theory, Methods and Applications, Vol. 27, No. 1 (1996), 97-114.

Karczewska A., "Statistical Solutions for Stochastic Burgers Equation", Statistics & Probability Letters 27 (1996), 305-311.

Karczewska A., "Statistical study of stochastic diffusion equation", Universitatis Jagiellonicae Acta Mathematica, Fasc. XXXII (1995), 201-211.

PREPRINTS

Karczewska, A., Rozmej, P., "Comment on the paper "The third-order perturbed Korteweg-de Vries equation for shallow water waves with a non-flat bottom" by M. Fokou, T.C. Kofane, A. Mohamadou and E. Yomba, Eur. Phys. J. Plus, 132, 410 (2017)", Preprint: arXiv:1804.01940.

Karczewska, A., Rozmej, P., "New exact superposition solutions to KdV2 equation", Preprint: arXiv:1804.02222.

Karczewska, A., Rozmej P., Infeld E., "Superposition solutions to the extended KdV equation for water surface waves", Preprint: arXiv:1708.05975.

Karczewska A., Szczecinski, M., "Martingale solution to stochastic extended Korteweg - de Vries equation", Preprint: arXiv:1708.03909.

Karczewska A., Szczecinski, M., "Existence of mild solution to stochastic extended Korteweg - de Vries equation ", Preprint: arXiv:1708.03907.

Karczewska A., Szczecinski, M., "Martingale solution to stochastic Korteweg - de Vries equation driven by Levy noise", Preprint: arXiv:1708.03902.

Karczewska, A., Infeld E., Rozmej P., Rowlands G., "Exact solitonic and periodic solutions of the extended KdV equation", Preprint: arXiv:1612.03847.

Karczewska, A., Rowlands G, Rozmej P., Infeld E., "Single soliton solution to the extended KdV equation over uneven depth", Preprint:arXiv:1612.05022.

Karczewska A., Szczecinski, M, Rozmej P., Boguniewicz, B."Finite Element Method for Stochastic Extended KdV Equations". Preprint:arXiv:1604.04226

Karczewska, A., Rozmej P., Szczecinski, M, Boguniewicz, B."Finite Element Method for Extended KdV Equations". Preprint:arXiv:1604.04105

Karczewska, A., Rozmej P., Infeld E., Rowlands, G.,"Adiabatic invariants of the extended KdV equation". Preprint: arXiv:1512.01194

Karczewska, A., Rozmej P., Infeld E.,"Energy invariant for shallow water waves and the Korteweg -- de Vries equation. Is energy always an invariant". Preprint: arXiv:1503.09089

Karczewska, A., Rozmej P., Infeld E.,"Shallow water soliton dynamics beyond KdV". Preprint:nlin.PS/1401.4859

Karczewska, A., Rozmej P., Rutkowski Ł.,"New nonlinear equation of KdV-type for a non-flat bottom". Preprint: nlin.PS/1401.4261

Karczewska A.,"Temporal and spatial regularity of solutions to stochastic Volterra equations of convolution type". Preprint: math.PR/1212.1257

**Karczewska, A., Rozmej P., "Exact superposition solutions to KdV2 equation" Advances in Mathematical Physics, vol. 2018, Article ID 5095482, 9 pages, (2018). DOI: 10.1155/2018/5095482.**