Front propagation in nonlinear parabolic equations

0434174 - MÚ 2015 RIV GB eng J - Journal Article
Feireisl, Eduard - Hilhorst, D. - Petzeltová, Hana - Takáč, P.
Front propagation in nonlinear parabolic equations.
Journal of the London Mathematical Society. Roč. 90, č. 2 (2014), s. 551-572. ISSN 0024-6107. E-ISSN 1469-7750
R&D Projects: GA ČR GA13-00522S
Institutional support: RVO:67985840
Keywords : nonlinear parabolic equations * front propagation * travelling wave
Subject RIV: BA - General Mathematics
Impact factor: 0.820, year: 2014
http://jlms.oxfordjournals.org/content/90/2/551

We study existence and stability of travelling waves for nonlinear convection–diffusion equations in the one-dimensional Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p -Laplacian and may be degenerate. We also prove that the solution converges to ±1 outside an interface which moves with constant velocity; our results include both generation and propagation of interface properties. In particular, unconditional stability is established with respect to initial data perturbations in L 1 (R).
Permanent Link: http://hdl.handle.net/11104/0238301