Solvability of some inhomogeneous parabolic equations.

摘要

The purpose of this thesis is to give necessary and almost sufficient conditions on the inhomogeneous, and potential terms of for which the Cauchy problem, Du-6tu+Vup+w=0 ux,0=u0 x. has a positive solution.;Here Deltau = i=1nuxi xi and V = V(x), w = w(x) ≥ 0 with V , w ∈ L1loc ; x ∈ RN and t > 0. The value of the results obtained are two-fold. Firstly, it brings a new level of parabolic abstractness to the corresponding elliptic work of [KV]. Secondly, it improves on the results in [BP].