TY - JOUR AU - Kersner, Róbert AU - Klincsik, Mihály AU - Zhanuzakova, Dinara TI - A competition system with nonlinear cross-diffusion: exact periodic patterns JF - REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS J2 - RACSAM REV R ACAD A VL - 116 PY - 2022 IS - 4 PG - 11 SN - 1578-7303 DO - 10.1007/s13398-022-01299-1 UR - https://m2.mtmt.hu/api/publication/33236539 ID - 33236539 AB - Our concern in this paper is to shed some additional light on the mechanism and the effect caused by the so called cross-diffusion. We consider a two-species reaction-diffusion (RD) system. Both "fluxes" contain the gradients of both unknown solutions. We show that-for some parameter range- there exist two different type of periodic stationary solutions. Using them, we are able to divide into parts the (eight-dimensional) parameter space and indicate the so called Turing domains where our solutions exist. The boundaries of these domains, in analogy with "bifurcation point", called "bifurcation surfaces". As it is commonly believed, these solutions are limits as t goes to infinity of the solutions of corresponding evolution system. In a forthcoming paper we shall give a detailed account about our numerical results concerning different kind of stability. Here we also show some numerical calculations making plausible that our solutions are in fact attractors with a large domain of attraction in the space of initial functions. LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Kersner, Róbert TI - Reply to comment on ‘Heat conduction: a telegraph-type model with self-similar behavior of solutions’ (2010 J. Phys. A: Math. Theor. 43 375210) JF - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL J2 - J PHYS A-MATH THEOR VL - 54 PY - 2021 IS - 8 PG - 1 SN - 1751-8113 DO - 10.1088/1751-8121/aba91c UR - https://m2.mtmt.hu/api/publication/31891062 ID - 31891062 N1 - doc type - wos: editorial doi - REPLY Scopus: note TT: Reply to comment on ‘Heat conduction: a telegraph-type model with self-similar behavior of solutions’ (2010 J. Phys. A: Math. Theor. 43 375210) LA - English DB - MTMT ER - TY - JOUR AU - Barna, Imre Ferenc AU - Kersner, Róbert TI - Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium JF - JOURNAL OF GENERALIZED LIE THEORY AND APPLICATIONS J2 - J GEN LIE THEORY APPL VL - 10 PY - 2016 IS - S2 PG - 4 SN - 1736-5279 DO - 10.4172/1736-4337.1000S2-010 UR - https://m2.mtmt.hu/api/publication/3175838 ID - 3175838 LA - English DB - MTMT ER - TY - JOUR AU - Svantnerné Sebestyén, Gabriella AU - Faragó, István AU - Horváth, Róbert AU - Kersner, Róbert AU - Klincsik, Mihály TI - Stability of patterns and of constant steady states for a cross-diffusion system JF - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS J2 - J COMPUT APPL MATH VL - 293 PY - 2016 SP - 208 EP - 216 PG - 9 SN - 0377-0427 DO - 10.1016/j.cam.2015.03.041 UR - https://m2.mtmt.hu/api/publication/2922088 ID - 2922088 LA - English DB - MTMT ER - TY - JOUR AU - B H, Gilding AU - Kersner, Róbert TI - On a nonlinear hyperbolic equation with a bistable reaction term JF - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS J2 - NONLINEAR ANAL-THEOR VL - 114 PY - 2015 SP - 169 EP - 185 PG - 17 SN - 0362-546X DO - 10.1016/j.na.2014.10.036 UR - https://m2.mtmt.hu/api/publication/3033623 ID - 3033623 N1 - Export Date: 1 March 2024 CODEN: NOAND Correspondence Address: Gilding, B.H.; Department of Mathematics, College of Science, Kuwait University, P.O. Box 5969, Kuwait LA - English DB - MTMT ER - TY - JOUR AU - M, Guedda AU - Kersner, Róbert AU - Klincsik, Mihály AU - E, Logak TI - EXACT WAVEFRONTS AND PERIODIC PATTERNS IN A COMPETITION SYSTEM WITH NONLINEAR DIFFUSION JF - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B J2 - DISCRETE CONT DYN-B VL - 19 PY - 2014 IS - 6 SP - 1589 EP - 1600 PG - 12 SN - 1531-3492 DO - 10.3934/dcdsb.2014.19.1589 UR - https://m2.mtmt.hu/api/publication/2907282 ID - 2907282 LA - English DB - MTMT ER - TY - JOUR AU - B H, Gilding AU - Kersner, Róbert TI - Wavefront solutions of a nonlinear telegraph equation JF - JOURNAL OF DIFFERENTIAL EQUATIONS J2 - J DIFFER EQUATIONS VL - 254 PY - 2013 IS - 2 SP - 599 EP - 636 PG - 38 SN - 0022-0396 DO - 10.1016/j.jde.2012.09.007 UR - https://m2.mtmt.hu/api/publication/3033625 ID - 3033625 LA - English DB - MTMT ER - TY - BOOK AU - Brian, H Gilding AU - Kersner, Róbert TI - Travelling waves in nonlinear diffusion-convection reaction ET - 0 PB - Birkhäuser Publishing Ltd. CY - Basel PY - 2012 SN - 9783034896382 UR - https://m2.mtmt.hu/api/publication/3187851 ID - 3187851 LA - English DB - MTMT ER - TY - CHAP AU - Kersner, Róbert AU - Klincsik, Mihály ED - Iványi, Péter TI - Patterns in reaction-diffusion systems T2 - Eight International PhD & DLA Symposium PB - University of Pécs Pollack Mihály Faculty of Engineering and Information Technology CY - Pécs SN - 9789637298486 PY - 2012 SP - 78 EP - 78 PG - 1 UR - https://m2.mtmt.hu/api/publication/3109433 ID - 3109433 LA - English DB - MTMT ER - TY - JOUR AU - Barna, I F AU - Kersner, Róbert TI - Heat conduction. A telegraph-type model with self-similar behavior of solutions II TS - A telegraph-type model with self-similar behavior of solutions II JF - ADVANCED STUDIES IN THEORETICAL PHYSICS J2 - ADV STUDIES VL - 5 PY - 2011 IS - 1-4 SP - 193 EP - 205 PG - 13 SN - 1313-1311 UR - https://m2.mtmt.hu/api/publication/1756137 ID - 1756137 AB - In our former study (J. Phys. A: Math. Theor. 43, (2010) 325210) we introduced a modified Fourier-Cattaneo law and derived a nonautonomous telegraph-type heat conduction equation which has desirable self-similar solution. Now we present a detailed in-depth analysis of this model and discuss additional analytic solutions for different parameters. The solutions have a very rich and interesting mathematical structure due to various special functions. LA - English DB - MTMT ER -