NONLOCAL MIXED PROBLEMS FOR SINGULAR PARABOLIC EQUATIONS

Abstract

Mixed problems with nonlocal boundary condition or with nonlocal initial con- ditions were studied by many mathematicians lately [3, 4, 5, 7]. The importance of problems with integral condition has been pointed out by Samarskii [8]. Mathematical modelling by evolution problems with nonlocal constraint is encountered in heat transmission theory, ther- moelasticity, chemical engineering, underground water flow, and plasma physics. In [1] the author derived a priori estimation of the solution for mixed problems with integral condition for singular parabolic equations, and in [2] it was proved that such problem is solvable. In this paper we prove a theorem about the existence and uniqueness of strong generalized solution of nonlocal mixed problems for singular parabolic equations.