We consider the local existence and the uniqueness of a weak solution of the initial boundary value problem to a convection–diffusion equation in a uniformly local function space Lr uloc,ρ(Ω), where the solution is not decaying at |x| → ∞. We show that the local existence and the uniqueness of a solution for the initial data in uniformly local Lr spaces and identify the Fujita-Weissler critical exponent for the local well-posedness found by Escobedo-Zuazua  is also valid for the uniformly local function class.
- Convection-diffusion equation
- Uniformly local Lebesgue spaces
- Weak solution
ASJC Scopus subject areas
- Applied Mathematics