Uniqueness classes of solutions of boundary value problems for nondivergent second order parabolic equations in noncylindrical domains (Q1813270)

The Dirichlet problem for a second order linear parabolic equation in an unbounded noncylindrical domain \(G\) is considered: \(\partial_ tu=\sum a_{ij}(x,t)\partial^ 2_{x_ ix_ j}u\), \(x,t\in G\); \(u|_ \gamma=0\). \(G\) is located in the layer \(G\subset\{x\in\mathbb{R}^ n\), \(- \varphi(| x|)<t<T<\infty\}\), \(n\geq 1\); with \(\overline\lim \varphi(s)/s^ 2=0\), \(s\to\infty\). The boundary \(\partial G\) consists of the plane \(t=T\) and a kind of parabolic surface \(\gamma\). The uniqueness of the solution of the problem is demonstrated in a Tichonov-Tacklind class.