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math.AP2020★ 1 cited
Long-time behavior of solutions to the generalized Allen-Cahn model with degenerate diffusivity
Raffaele Folino, Luis F. López Ríos, Ramón G. Plaza
The generalized Allen-Cahn equation, \[ u_t=\varepsilon^2(D(u)u_x)_x-\frac{\varepsilon^2}2D'(u)u_x^2-F'(u), \] with nonlinear diffusion, , and potential, , of t…
math.AP2020★ 6 cited
Long time dynamics of solutions to -Laplacian diffusion problems with bistable reaction terms
Raffaele Folino, Ramón G. Plaza, Marta Strani
This paper establishes the emergence of slowly moving transition layer solutions for the -Laplacian (nonlinear) evolution equation, \[ u_t = \varepsilon^p(|u_x|^{p-2}u_x)_x - F'…