Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem
Viscosity solutions and standard Riemann semigroup for conservation laws with boundary
Viscosity solutions of elliptic partial differential equations.
Viscosity solutions of fully nonlinear functional parabolic PDE.
Viscosity solutions of nonlinear systems of degenerated elliptic equations of second order.
Viscosity solutions of the Cauchy problem for second-order nonlinear partial differential equations in Hilbert spaces.
Viscosity subsolutions and supersolutions for non-uniformly and degenerate elliptic equations
In the present paper we study the Dirichlet boundary value problem for quasilinear elliptic equations including non-uniformly and degenerate ones. In particular, we consider mean curvature equation and pseudo p-Laplace equation as well. It is well-known that the proof of the existence of continuous viscosity solutions is based on Ishii’s implementation of Perron’s method. In order to use this method one has to produce suitable subsolution and supersolution. Here we introduce new methods to construct...
Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients
We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is with (expansive case not included in our first result), thus resulting in an infinity of weak solutions. Proving that this problem is uniformly Evans-stable, we show that...
Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case.
Viscous profiles of vortex patches
Viscous Shock Capturing in a Time-Explicit Discontinuous Galerkin Method
We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG) methods. The output of this detector is a reliably scaled, element-wise smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the...
Viscous-inviscid coupled problem with interfacial data.
Vitesse de convergence vers le réel des résonances
Volume Filling Effect in Modelling Chemotaxis
The oriented movement of biological cells or organisms in response to a chemical gradient is called chemotaxis. The most interesting situation related to self-organization phenomenon takes place when the cells detect and response to a chemical which is secreted by themselves. Since pioneering works of Patlak (1953) and Keller and Segel (1970) many particularized models have been proposed to describe the aggregation phase of this process. Most of...
Volume mean values of subtemperatures
Several authors have found the characteristic mean value formula for temperatures over heat spheres. Those who derived a corresponding formula over heat balls have all chosen different mean values. In this paper we discuss an infinity of possible means over heat balls, and show that, in the wider context of subtemperatures, some are more desirable than others.
Von Kármán equations. III. Solvability of the von Kármán equations with conditions for geometry of the boundary of the domain
Solvability of the general boundary value problem for von Kármán system of nonlinear equations is studied. The problem is reduced to an operator equation. It is shown that the corresponding functional of energy is coercive and weakly lower semicontinuous. Then the functional of energy attains absolute minimum which is a variational solution of the problem.
Von Neumann analysis of linearized discrete Tzitzeica PDE.
Vortex analysis of the periodic Ginzburg-Landau model
Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part I: Study of the perturbed Ginzburg–Landau equation
We study vortices for solutions of the perturbed Ginzburg–Landau equations where is estimated in . We prove upper bounds for the Ginzburg–Landau energy in terms of , and obtain lower bounds for in terms of the vortices when these form “unbalanced clusters” where . These results will serve in Part II of this paper to provide estimates on the energy-dissipation rates for solutions of the Ginzburg–Landau heat flow, which allow one to study various phenomena occurring in this flow, including...
Vortex collisions and energy-dissipation rates in the Ginzburg–Landau heat flow. Part II: The dynamics
We deduce from the first part of this paper [S1] estimates on the energy-dissipation rates for solutions of the Ginzburg–Landau heat flow, which allow us to study various phenomena occurring in this flow, including vortex collisions; they allow in particular extending the dynamical law of vortices past collision times.