Nonlocal in time problem for anisotropic parabolic equations with variable exponents of nonlinearities. (English) Zbl 1411.35177

Buhrii, Oleh; Buhrii, Nataliya

J. Math. Anal. Appl. 473, No. 2, 695-711 (2019).

Summary: In this study, we consider nonlinear parabolic equations with variable exponents of the nonlinearities. The nonlocal problem for these equations is investigated, and the existence and uniqueness theorems are proved for the problem.

MSC:

35K59	Quasilinear parabolic equations
35A01	Existence problems for PDEs: global existence, local existence, non-existence
35A02	Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
35K20	Initial-boundary value problems for second-order parabolic equations

Keywords:

generalized Lebesgue and Sobolev spaces; nonlinear parabolic equation; nonlocal in time problem; variable exponents of nonlinearities

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