On periodic solutions of a parabolic problem with a small parameter at the derivatives. (Russian, English) Zbl 1136.35306

Vasil’eva, A. B.

Zh. Vychisl. Mat. Mat. Fiz. 43, No. 7, 975-986 (2003); translation in Comput. Math. Math. Phys. 43, No. 7, 932-943 (2003).

A boundary value problem is considered for a singularly perturbed parabolic equation that involves a small parameter multiplying all derivatives and degenerates into a finite equation when the parameter is equal to zero. An existence theorem is proved for a periodic solution with an internal layer, i.e., for a steplike contrast structure. A theorem on passage to the limit when the small parameter vanishes is proved as well.

Reviewer: Andrei Zemskov (Moskva)

MSC:

35B10	Periodic solutions to PDEs
35B25	Singular perturbations in context of PDEs
35K55	Nonlinear parabolic equations

Keywords:

parabolic singularly perturbed equations; small parameter; periodic solution; passage to the limit; contrast structure