EUDML

Currently displaying 1 – 7 of 7

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A Stefan problem for the heat equation subject to an integral condition

Elena Comparini; Domingo A. Tarzia — 1985

Rendiconti del Seminario Matematico della Università di Padova

A spatially inhomogeneous diffusion problem with strong absorption

Riccardo Ricci; Domingo A. Tarzia — 2003

Bollettino dell'Unione Matematica Italiana

We study the asymptotic behaviour ( $t \to + \infty$ ) of the solutions of a nonlinear diffusion problem with strong absorption. We prove convergence to the stationary solution in the $L^{\infty}$ by means of an appropriate family of sub and supersolutions. In appendix we prove the well posedness of the problem.

Explicit solutions for a one-phase Stefan problem with temperature-dependent thermal conductivity

María F. Natale; Domingo A. Tarzia — 2006

Bollettino dell'Unione Matematica Italiana

We study a one-phase Stefan problem for a semi-infinite material with temperature-dependent thermal conductivity with a constant temperature or a heat flux condition of the type $-q_{0}/\sqrt{t}$ ( $q_{0}>0$ ) at the fixed face $x=0$ . We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for $t\geq t_{0}>0$ with $t_{0}$ an arbitrary positive time. These explicit solutions are obtained through the unique solution of an integral equation with the time as a parameter....

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

Mircea Sofonea; Domingo A. Tarzia — 2022

Applications of Mathematics

We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain $D \subset ℝ^{d}$ and its weak formulation is in the form of a hemivariational inequality for the temperature field, denoted by $𝒫$ . We associate to Problem $𝒫$ an optimal control problem, denoted by $𝒬$ . Then, using appropriate Tykhonov triples, governed by a nonlinear operator $G$ and a convex $\tilde{K}$ , we provide results concerning the well-posedness of problems...