Théorie spectrale d'une classe d'opérateurs elliptiques dégénérés non nécessairement auto-adjoint
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
Theory of completely integrable equations
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...
Thermo-viscous fluid flow in porous slab bounded between two impermeable parallel plates in relative motion: Four stage algorithm approach
The problem of an approximate solution of thermo-viscous fluid flow in a porous slab bounded between two impermeable parallel plates in relative motion is examined in this paper. The two plates are kept at two different temperatures and the flow is generated by a constant pressure gradient together with the motion of one of the plates relative to the other. The velocity and temperature distributions have been obtained by a four-stage algorithm approach. It is worth mentioning that reverse effects...
Thick obstacle problems with dynamic adhesive contact
In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the Kelvin-Voigt type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...
Thin vortex tubes in the stationary Euler equation
In this paper we outline some recent results concerning the existence of steady solutions to the Euler equation in with a prescribed set of (possibly knotted and linked) thin vortex tubes.
Thinness and the heat equation
Third boundary value problem for the heat equation. I.
Third boundary value problem for the heat equation. II.
Three applications of differential equations in turbulence research
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 nodal solutions of singularly perturbed elliptic equations on domains without topology
Three non-trival solutions of anticoercive boundary value problems for the Pseudo-Laplace-operator.
Three solutions for a nonlinear Neumann boundary value problem
The aim of this paper is to establish the existence of at least three solutions for the nonlinear Neumann boundary-value problem involving the p(x)-Laplacian of the form in Ω, on ∂Ω. Our technical approach is based on the three critical points theorem due to Ricceri.
Three solutions for quasilinear equations in near resonance.
Three solutions for singular -Laplacian type equations.