Author/Authors :
Jenaliyev, M.T. Institute of Mathematics and Mathematical Modeling, Pushkin, Almaty, Kazakhstan , Ramazanov, M.I. Buketov Karaganda State University, Karaganda, Kazakhstan , Iskakov, S.A. Buketov Karaganda State University, Karaganda, Kazakhstan
Abstract :
In this paper we study a homogeneous boundary value problem for the heat
equation in a noncylindrical domain with the special boundary conditions. The problem
under consideration is useful for solving the single-phase Stefan problem. It has been shown
that this homogeneous problem has a nontrivial solution up to constant factor in the weight
class of essentially bounded functions. A class of functions in which this problem has only a
trivial solution is found. Thus, a class of functions in which the corresponding inhomogeneous
problem is uniquely solvable is defined.
