Tykhonov well-posedness of a heat transfer problem with unilateral constraints

SOFONEA, MIRCEA; D. A. TARZIA

APPLICATIONS OF MATHEMATICS

ACAD SCIENCES CZECH REPUBLIC

Año: 2022 vol. 67 p. 167 - 197

0862-7940

We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain D in IRdand its weak formulation is in the form of a hemivariational inequality for the temperature eld,denoted by P. We associate to Problem P an optimal control problem, denoted by Q. Then, usingappropriate Tykhonov triples, governed by a nonlinear operator G and a convex eK, we provide results concerning the well-posedness of problems P and Q. Our main results are Theorems 14 and 18, together with their corollaries. Their proofs are based on arguments of compactness, lower semicontinuity and pseudomonotonicity. Moreover, we consider three relevant perturbations of the heat transfer boundary valued problem which lead to penalty versions of Problem P, constructed with particular choices of G and eK. . We prove that Theorems 14 and 18 as well as their corollaries can be applied in the study of these problems, in order to obtain various convergence results.