@article{MTMT:33236539,
	title = {A competition system with nonlinear cross-diffusion: exact periodic patterns},
	url = {https://m2.mtmt.hu/api/publication/33236539},
	author = {Kersner, Róbert and Klincsik, Mihály and Zhanuzakova, Dinara},
	doi = {10.1007/s13398-022-01299-1},
	journal-iso = {RACSAM REV R ACAD A},
	journal = {REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS},
	volume = {116},
	unique-id = {33236539},
	issn = {1578-7303},
	abstract = {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.},
	keywords = {pattern formation; Periodic stationary solutions; Stability of patterns; Cross-diffusion; Reaction-diffusion (RD )systems},
	year = {2022},
	eissn = {1579-1505}
}

@article{MTMT:31891062,
	title = {Reply to comment on ‘Heat conduction: a telegraph-type model with self-similar behavior of solutions’ (2010 J. Phys. A: Math. Theor. 43 375210)},
	url = {https://m2.mtmt.hu/api/publication/31891062},
	author = {Barna, Imre Ferenc and Kersner, Róbert},
	doi = {10.1088/1751-8121/aba91c},
	journal-iso = {J PHYS A-MATH THEOR},
	journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL},
	volume = {54},
	unique-id = {31891062},
	issn = {1751-8113},
	keywords = {Physics, Multidisciplinary},
	year = {2021},
	eissn = {1751-8121},
	orcid-numbers = {Barna, Imre Ferenc/0000-0001-6206-3910}
}

@article{MTMT:3175838,
	title = {Heat Conduction: Hyperbolic Self-similar Shock-waves in Solid Medium},
	url = {https://m2.mtmt.hu/api/publication/3175838},
	author = {Barna, Imre Ferenc and Kersner, Róbert},
	doi = {10.4172/1736-4337.1000S2-010},
	journal-iso = {J GEN LIE THEORY APPL},
	journal = {JOURNAL OF GENERALIZED LIE THEORY AND APPLICATIONS},
	volume = {10},
	unique-id = {3175838},
	issn = {1736-5279},
	year = {2016},
	eissn = {1736-4337},
	orcid-numbers = {Barna, Imre Ferenc/0000-0001-6206-3910}
}

@article{MTMT:2922088,
	title = {Stability of patterns and of constant steady states for a cross-diffusion system},
	url = {https://m2.mtmt.hu/api/publication/2922088},
	author = {Svantnerné Sebestyén, Gabriella and Faragó, István and Horváth, Róbert and Kersner, Róbert and Klincsik, Mihály},
	doi = {10.1016/j.cam.2015.03.041},
	journal-iso = {J COMPUT APPL MATH},
	journal = {JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS},
	volume = {293},
	unique-id = {2922088},
	issn = {0377-0427},
	keywords = {Nonlinear equations; DIFFUSION; nonlinear systems; System stability; Differential equations; steady state; stationary solutions; periodic solutions; Numerical models; System of partial differential equations; Periodic solution; Periodic stationary solutions; Cross-diffusion system; Abnormal tissues; Stability of patterns; Nonlinear systems of PDEs; Cross-diffusion},
	year = {2016},
	eissn = {1879-1778},
	pages = {208-216},
	orcid-numbers = {Faragó, István/0000-0002-4615-7615}
}

@article{MTMT:3033623,
	title = {On a nonlinear hyperbolic equation with a bistable reaction term},
	url = {https://m2.mtmt.hu/api/publication/3033623},
	author = {B H, Gilding and Kersner, Róbert},
	doi = {10.1016/j.na.2014.10.036},
	journal-iso = {NONLINEAR ANAL-THEOR},
	journal = {NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS},
	volume = {114},
	unique-id = {3033623},
	issn = {0362-546X},
	year = {2015},
	eissn = {1873-5215},
	pages = {169-185}
}

@article{MTMT:2907282,
	title = {EXACT WAVEFRONTS AND PERIODIC PATTERNS IN A COMPETITION SYSTEM WITH NONLINEAR DIFFUSION},
	url = {https://m2.mtmt.hu/api/publication/2907282},
	author = {M, Guedda and Kersner, Róbert and Klincsik, Mihály and E, Logak},
	doi = {10.3934/dcdsb.2014.19.1589},
	journal-iso = {DISCRETE CONT DYN-B},
	journal = {DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B},
	volume = {19},
	unique-id = {2907282},
	issn = {1531-3492},
	year = {2014},
	eissn = {1553-524X},
	pages = {1589-1600}
}

@article{MTMT:3033625,
	title = {Wavefront solutions of a nonlinear telegraph equation},
	url = {https://m2.mtmt.hu/api/publication/3033625},
	author = {B H, Gilding and Kersner, Róbert},
	doi = {10.1016/j.jde.2012.09.007},
	journal-iso = {J DIFFER EQUATIONS},
	journal = {JOURNAL OF DIFFERENTIAL EQUATIONS},
	volume = {254},
	unique-id = {3033625},
	issn = {0022-0396},
	year = {2013},
	eissn = {1090-2732},
	pages = {599-636}
}

@book{MTMT:3187851,
	title = {Travelling waves in nonlinear diffusion-convection reaction},
	url = {https://m2.mtmt.hu/api/publication/3187851},
	isbn = {9783034896382},
	author = {Brian, H Gilding and Kersner, Róbert},
	publisher = {Birkhäuser Publishing Ltd.},
	unique-id = {3187851},
	year = {2012}
}

@{MTMT:3109433,
	title = {Patterns in reaction-diffusion systems},
	url = {https://m2.mtmt.hu/api/publication/3109433},
	author = {Kersner, Róbert and Klincsik, Mihály},
	booktitle = {Eight International PhD & DLA Symposium},
	unique-id = {3109433},
	year = {2012},
	pages = {78-78}
}

@article{MTMT:1756137,
	title = {Heat conduction. A telegraph-type model with self-similar behavior of solutions II},
	url = {https://m2.mtmt.hu/api/publication/1756137},
	author = {Barna, I F and Kersner, Róbert},
	journal-iso = {ADV STUDIES},
	journal = {ADVANCED STUDIES IN THEORETICAL PHYSICS},
	volume = {5},
	unique-id = {1756137},
	issn = {1313-1311},
	abstract = {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.},
	keywords = {Telegraph-type equation; Self-similar solution; Heat propagation},
	year = {2011},
	eissn = {1314-7609},
	pages = {193-205}
}