UNIQUENESS OF SOLUTIONS OF PARABOLIC SEMILINEAR NONLOCAL-BOUNDARY PROBLEMS

The purpose of the paper is to give two theorems about the uniqueness of solutions of parabolic semilinear nonlocal-boundary problems. The paper is a continuation of previous papers by Byszewski and the generalization of some results from [R. Rabczuk, "Introduction to Differential Inequalities," PWN, Warsaw, 1976 [Polish]; J. Chabrowski, On nonlocal problems for parabolic equations, Nagoya Math. J. 93 (1984), 109-131], The theorems obtained in this paper can be applied in the theories of diffusion and heat conduction with better effects than the analogous theorems about parabolic initial-boundary problems and than the analogous theorems about parabolic periodic-boundary problems. © 1992.