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

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.


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