Rothe time-discretization method for the semilinear heat equation subject to a nonlocal boundary condition

[摘要] This paper is devoted to prove, in a nonclassical function space, the weaksolvability of a mixed problem which combines a Neumann condition and an integralboundary condition for the semilinear one-dimensional heat equation. Theinvestigation is made by means of approximation by the Rothe method which isbased on a semidiscretization of the given problem with respect to the time variable.

[学科分类] 应用数学