Dr hab. Anna Karczewska, Prof. UZ
Faculty of Mathematics, Computer Science and Econometrics
University of Zielona Góra, ul. Szafrana 4a, PL 65-516 Zielona Góra, Poland
THIS IS NOT ME!
Telephone: (+48) (068) 32 82 822  Fax: (+48) (068) 32 82 875
A.Karczewska@wmie.uz.zgora.pl

RESEARCH INTERESTS

PhD promotions

MONOGRAPHS

Hot topics

SUBMITTED PAPERS

PUBLISHED PAPERS

  • Rozmej, P., Karczewska, A., "KdV, extended KdV, 5th-order KdV and Gardner equations generalized for uneven bottom versus corresponding Boussinesq’s equations", Advances in Nonlinear Dynamics, Proceedings of the Second International Nonlinear Dynamics Conference (NODYCON 2021), Volume 3, 443-453 (2022). Springer International Publishing AG. DOI: 10.1007/978-3-030-81170-9

  • Karczewska, A., Rozmej, P., "Inverted solutions of KdV-type and Gardner equations", Acta Physica Polonica A, Vol. 140, no. 5, 445-449 (2021) DOI: 10.12693/APhysPolA.140.445

  • Rozmej, P., Karczewska, A., "Comment on "Two-dimensional third- and fifth-order nonlinear evolution equations for shallow water waves with surface tension" [Nonlinear Dyn, doi:10.1007/s11071-017-3938-7]", Nonlinear Dynamics, Vol. 105, no. 5, 2855–2860 (2021) DOI: 10.1007/s11071-021-06716-5.

  • Karczewska, A., Rozmej P., "Can simple KdV-type equations be derived for shallow water problem with bottom bathymetry?" Communications in Nonlinear Science and Numerical Simulations, Vol. 82 (2020), 105073. DOI: 10.1016/j.cnsns.2019.105073 .

  • Karczewska, A., Rozmej, P., "Generalized KdV-type equations versus Boussinesq's equations for uneven bottom - numerical study", Computational Methods in Science and Technology, Vol. 26, no. 4, 121-136 (2020) DOI: 10.12921/cmst.2020.0000036

  • Karczewska, A., Rozmej, P., "Remarks on existence/nonexistence of analytic solutions to higher order KdV equations", Acta Physica Polonica A, Vol. 136, no. 6, 910-915 (2019). DOI: 10.12693/APhysPolA.136.910

  • Karczewska, A., Szczeciński M., "Stochastic extended Korteweg-de Vries equation", Journal of Mathematical Sciences and Modelling, Vol. 2 (2) (2019) pp. 74-81 DOI: 10.33187/jmsm.459461 .

  • Karczewska A., Szczeciński M., "Martingale solution to stochastic extended Korteweg - de Vries equation", Advances in Pure Mathematics, Vol. 8, (2018), pp. 863-878. DOI: 10.4236/apm.2018.812053 .

  • Karczewska, A., Rozmej P., , "The new extended KdV equation for the case of an uneven bottom" Computational Methods in Science and Technology, Vol. 24 (4), (2018), pp. 221-225. DOI: 10.12921/cmst.2018.0000057 .

  • Rozmej P., Karczewska, A. , "Adiabatic invariants of second order Korteweg - de Vries type equation" Chapter in: Nonlinear Systems, Vol. 1 : Mathematical Theory and Computation Methods, Springer, 2018, pp. 175-205. PDF-file .

  • Karczewska, A., Infeld E., Rowlands G., Rozmej P. , "Exact cnoidal solutions to the extended KdV equation", Acta Physica Polonica A, Vol. 133, No. 5, 1191-1199 (2018). DOI: 10.12693/APhysPolA.133.1191

  • 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., "The only true (2+1)-dimensional nonlocal KdV, fifth-order KdV, and Gardner equations derived from the ideal fluid model", Preprint: arXiv:2206.08964.

  • Karczewska, A., Rozmej, P., "Boussinesq's equations for (2+1)-dimensional gravity-surface waves in an ideal fluid model", Preprint: arXiv:2108.11150 .

  • Karczewska, A., Rozmej, P., "Inverted solutions of KdV-type and Gardner equations", Preprint: arXiv:2107.14237 .

  • Rozmej, P., Karczewska, A., "Comment on "Two-dimensional third- and fifth-order nonlinear evolution equations for shallow water waves with surface tension" [Nonlinear Dyn, doi:10.1007/s11071-017-3938-7]", Preprint: arXiv:2105.08519 .

  • Karczewska, A., Rozmej, P., "Signatures of chaotic dynamics in wave motion according to the extended KdV equation", Preprint: arXiv:2101.06632 .

  • Karczewska, A., Szczeciński. M., "Martingale solution of stochastic hybrid Korteweg - de Vries - Burgers equation", Preprint: arXiv:2101.6628 .

  • Karczewska, A., Rozmej, P., "Generalized KdV-type equations versus Boussinesq's equations for uneven bottom - numerical study", Preprint: arXiv:2007.01267 .

  • Karczewska, A., Rozmej, P., "What kinds of KdV-type equations are allowed by an uneven bottom", Preprint: arXiv:1903.890.

  • Karczewska, A., Rozmej, P., " Remarks on existence/nonexistence of analytic solutions to higher order KdV equations", Preprint: arXiv:1901.00001.

  • Rozmej, P., Karczewska, A., "Extended KdV equation for the case of uneven bottom", Preprint: arXiv:1810.07183.

  • 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. Kofan\'e, A. Mohamadou and E. Yomba, Eur. Phys. J. Plus, 132, 410 (2017) ", Preprint: arXiv:1804.19400.

  • 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., Szczeciński, M., "Martingale solution to stochastic extended Korteweg - de Vries equation", Preprint: arXiv:1708.03909.

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

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

  • Karczewska, A., Rozmej P., Szczeciński, 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 22, 2022 by A.Karczewska@wmie.uz.zgora.pl