Existence of weak solutions to a convection–diffusion equation in amalgam spaces

[摘要] We consider the local existence and uniqueness of a weak solution for a convection–diffusion equation in amalgam spaces. We establish the local existence and uniqueness of solution for the initial condition in amalgam spaces. Furthermore, we prove the validity of the Fujita–Weissler critical exponent for local existence and uniqueness of solution in the amalgam function class that is identified by Escobedo and Zuazua (J Funct Anal 100:119–161, 1991).

[发布日期] 2022-11-29

[关键词] Convection–diffusion equations;Amalgam spaces;Weak solution;Uniqueness;35A01;35K55;35D30