On a nonstationary model of a catalytic process in a fluidized bed.
On a numerical approach to Stefan-like problems.
On a numerical model for diffusion-controlled growth and dissolution of spherical precipitates.
On a parabolic integrodifferential equation of Barbashin type
In the present paper we study some basic qualitative properties of solutions of a nonlinear parabolic integrodifferential equation of Barbashin type which occurs frequently in applications. The fundamental integral inequality with explicit estimate is used to establish the results.
On a parabolic problem with nonlinear Newton boundary conditions
The paper is concerned with the study of a parabolic initial-boundary value problem with nonlinear Newton boundary condition considered in a two-dimensional domain. The goal is to prove the existence and uniqueness of a weak solution to the problem in the case when the nonlinearity in the Newton boundary condition does not satisfy any monotonicity condition and to analyze the finite element approximation.
On a parabolic strongly nonlinear problem on manifolds.
On a Parabolic Symmetry Problem.
On a parabolic-hyperbolic Penrose-Fife phase-field system.
On a parallel implementation of the mortar element method
On a Parallel Implementation of the Mortar Element Method
We discuss a parallel implementation of the domain decomposition method based on the macro-hybrid formulation of a second order elliptic equation and on an approximation by the mortar element method. The discretization leads to an algebraic saddle- point problem. An iterative method with a block- diagonal preconditioner is used for solving the saddle- point problem. A parallel implementation of the method is emphasized. Finally the results of numerical experiments are presented.
On a partial differential equation involving the jacobian determinant
On a perturbed Dirichlet problem for a nonlocal differential equation of Kirchhoff type.
On a phase transition model of Penrose-Fife type
We deal with a Penrose-Fife type model for phase transition. We assume a rather general constitutive low for the heat flux and treat the Dirichlet and Neumann boundary condition for the temperature. Some of our proofs apply to different types of boundary conditions as well and improve some results existing in the literature.
On a phase-field model with a logarithmic nonlinearity
Our aim in this paper is to study the existence of solutions to a phase-field system based on the Maxwell-Cattaneo heat conduction law, with a logarithmic nonlinearity. In particular, we prove, in one and two space dimensions, the existence of a solution which is separated from the singularities of the nonlinear term.
On a plane heat-conductivity theory problem with mixed boundary conditions.
On a possibility of generalization of the Hopf lemma to the case of the Navier-Stokes system with nonzero flows.
On a posteriori error estimators in the infinite element method on anisotropic meshes.
On a potential problem with incident wave as a field source
On a priori estimates for positive solutions of a semilinear biharmonic equation in a ball
On a probabilistic interpretation of shape derivatives of Dirichlet groundstates with application to Fermion nodes
This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the normal derivative of the groundstate on the boundary. We then propose to use this formulation in the...