The thermistor obstacle problem with periodic data
The Total Variation of Solutions of Parabolic Differential Equations and a Maximum Principle in Unbounded Domains.
The use of linear approximation scheme for solving the Stefan problem
This paper deals with the linear approximation scheme to approximate a singular parabolic problem: the two-phase Stefan problem on a domain consisting of two components with imperfect contact. The results of some numerical experiments and comparisons are presented. The method was used to determine the temperature of steel in the process of continuous casting.
The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.
In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.
The Wolff gradient bound for degenerate parabolic equations
The spatial gradient of solutions to non-homogeneous and degenerate parabolic equations of -Laplacean type can be pointwise estimated by natural Wolff potentials of the right hand side measure.
The zero set of a solution of a parabolic equation.
Theorems on -dimensional Laplace transforms and their applications.
Theoretical analysis of a model of the thermal boundary layer with drag.
Thermistor problem: a nonlocal parabolic problem.
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful successive...
Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion*
We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful...
Thinness and the heat equation
Third boundary value problem for the heat equation. I.
Third boundary value problem for the heat equation. II.
Three cylinder inequalities and unique continuation properties for parabolic equations
We prove the following unique continuation property. Let be a solution of a second order linear parabolic equation and a segment parallel to the -axis. If has a zero of order faster than any non constant and time independent polynomial at each point of then vanishes in each point, , such that the plane has a non empty intersection with .
Three-level difference schemes on non-uniform in time grids.
Time and space Sobolev regularity of solutions to homogeneous parabolic equations
We give necessary and sufficient conditions on the initial data such that the solutions of parabolic equations have a prescribed Sobolev regularity in time and space.
Time averaging for random nonlinear abstract parabolic equations.
Time decay of solutions to the Schrödinger equation in exterior domains. II
Time decay of solutions to the Schrödinger equation in exterior domains. I