Degenerating parabolic equations with a variable direction of evolution

Abstract

The aim of the paper is to study the solvability in the classes of regular solutions of boundary value problems for differential equations φ(t)ut − ψ(t)∆u + c(x, t)u = f (x, t) (x ∈ Ω ⊂ R n , 0 < t < T). A feature of these equations is that the function φ(t) in them can arbitrarily change the sign on the segment [0, T ], while the function ψ(t) is nonnegative for t ∈ [0, T ]. For the problems under consideration, we prove existence and uniqueness theorems.