Initial value problems for diffusion equations with singular potential

Original · EN

Let V be a nonnegative locally bounded function defined in Q∞:=ⁿ×(0,∞). We study under what conditions on V and on a Radon measure in Rᵈ does it exist a function which satisfies ∂ₜ u- u+ Vu=0 in Q∞ and u(.,0)=. We prove the existence of a subcritical case in which any measure is admissible and a supercritical case where capacitary conditions are needed. We obtain a general representation theorem of positive solutions when t V(x,t) is bounded and we prove the existence of an initial trace in the class of outer regular Borel measures.