@article{MTMT:1755719, title = {Interface dynamics of the Fisher equation with degenerate diffusion}, url = {https://m2.mtmt.hu/api/publication/1755719}, author = {D, Hilhorst and Kersner, Róbert and E, Logak and M, Mimura}, journal-iso = {ELECTR J DIFFER EQUAT}, journal = {ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS}, volume = {244}, unique-id = {1755719}, issn = {1072-6691}, year = {2008}, eissn = {1550-6150}, pages = {2870-2889} } @article{MTMT:1788513, title = {Interface dynamics of the Fisher equation with degenerate diffusion}, url = {https://m2.mtmt.hu/api/publication/1788513}, author = {Hilhorst, D and Kersner, Róbert and Logak, E and Mimura, M}, doi = {10.1016/j.jde.2008.02.018}, journal-iso = {J DIFFER EQUATIONS}, journal = {JOURNAL OF DIFFERENTIAL EQUATIONS}, volume = {244}, unique-id = {1788513}, issn = {0022-0396}, abstract = {We consider a degenerate parabolic reaction-diffusion equation with a monostable nonlinearity arising in population dynamics. In some suitable scaling limit, we prove the generation and propagation of an interface with constant normal velocity in the case that the initial condition has a convex compact support. © 2008 Elsevier Inc. All rights reserved.}, keywords = {population dynamics; Sharp interface limit; Reaction-diffusion equation; Nonlinear diffusion; Fisher equation; Finite speed of propagation}, year = {2008}, eissn = {1090-2732}, pages = {2870-2889} } @article{MTMT:1756234, title = {A fisher/KPP-type equation with density-dependent diffusion and convection: Travelling-wave solutions}, url = {https://m2.mtmt.hu/api/publication/1756234}, author = {Gilding, B H and Kersner, Róbert}, doi = {10.1088/0305-4470/38/15/009}, journal-iso = {J PHYS A-MATH GEN}, journal = {JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL}, volume = {38}, unique-id = {1756234}, issn = {0305-4470}, abstract = {This paper concerns processes described by a nonlinear partial differential equation that is an extension of the Fisher and KPP equations including density-dependent diffusion and nonlinear convection. The set of wave speeds forwhich the equation admits a wavefront connecting its stable and unstable equilibrium states is characterized. There is a minimal wave speed. For this wave speed there is a unique wavefront which can be found explicitly. It displays a sharp propagation front. For all greater wave speeds there is a unique wavefront which does not possess this property. For such waves, the asymptotic behaviour as the equilibrium states are approached is determined. © 2005 IOP Publishing Ltd.}, year = {2005}, eissn = {1361-6447}, pages = {3367-3379} } @article{MTMT:163288, title = {Stability of travelling waves for degenerate reaction-diffusion equations of KPP-type}, url = {https://m2.mtmt.hu/api/publication/163288}, author = {Biró, Zsolt Péter}, journal-iso = {ADV NONLINEAR STUD}, journal = {ADVANCED NONLINEAR STUDIES}, volume = {2}, unique-id = {163288}, issn = {1536-1365}, year = {2002}, eissn = {2169-0375}, pages = {357-371} }