Internal Layer Solutions in Quasilinear Integro-Differential Equations

Nikolai N. Nefedov , Oleh E. Omel'chenko , Lutz Recke

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976), 16, 27 pages

MSC 2000

35B25 Singular perturbations

35K60 Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE

45K05 Integro-partial differential equations

Abstract
The Dirichlet problem for a class of singularly perturbed quasilinear parabolic integro-differential equations is considered. For that problem an asymptotic expansion for a new class of solutions, which have internal layers, is constructed. Concerning those solutions, theorems on existence, local uniqueness and stability are proved.