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Wave propagation under curvature effects in a heterogeneous medium. (English) Zbl 0878.35009
This paper is concerned with the evolution of an interface propagating with a curvature-dependent speed, in a heterogeneous medium. The model equation is of quasilinear parabolic type with a curvature coefficient \(\varepsilon\). Working in a periodic context, we show the convergence of the solution of the initial-boundary value problem to a travelling wave solution. The behaviour of the corresponding steady speed is also investigated as \(\varepsilon\) goes to zero and we recover known results concerning the resulting Hamilton-Jacobi equation.
Reviewer: G.Namah (Bordeaux)

35B10 Periodic solutions to PDEs
35K55 Nonlinear parabolic equations
35B25 Singular perturbations in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
Full Text: DOI
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