EXISTENCE AND UNIQUENESS OF ABLOW-UP SOLUTION FOR A PARABOLIC PROBLEM WITH A LOCALIZED NONLINEAR TERM VIA SEMIGROUP THEORY

摘要

Here, we use the semigroup theory to establish the existence, unique-ness and blow-up for a classical solution of a semilinear parabolic problem with localized nonlinear term— a locally Lipschitz continuous function of the value of the solution at a point of a 1-dimensional domain. Our method, which uses Sobolev spaces and fractional power of operators, is in contrast with the classical ones (Green functions) which supply similar results in 1-dimensional settings.