Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face.
Exact solutions for nonclassical Stefan problems.
On a convex combination of solutions to elliptic variational inequalities.
A Stefan problem for the heat equation subject to an integral condition
A spatially inhomogeneous diffusion problem with strong absorption
We study the asymptotic behaviour () of the solutions of a nonlinear diffusion problem with strong absorption. We prove convergence to the stationary solution in the 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
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 () at the fixed face . We obtain in both cases sufficient conditions for data in order to have a parametric representation of the solution of the similarity type for with 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
We consider an elliptic boundary value problem with unilateral constraints and subdifferential boundary conditions. The problem describes the heat transfer in a domain and its weak formulation is in the form of a hemivariational inequality for the temperature field, denoted by . We associate to Problem an optimal control problem, denoted by . Then, using appropriate Tykhonov triples, governed by a nonlinear operator and a convex , we provide results concerning the well-posedness of problems...
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