Front propagation in nonlinear parabolic equations
Eduard Feireisl, Dorothea Hilhorst, Hana Petzeltová, Peter Takáč · Journal of the London Mathematical Society · 2014
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 ) .