Valeurs propres de problèmes aux limites elliptiques irréguliers
Valeurs propres d'une classe d'équations différentielles singulières sur une demi-droite
Valeurs propres d'une classe d'équations différentielles singulières sur une demi-droite
Variation of a nonlinear temperature field connected with the coefficient of heat conductivity.
Variation of constants formula for functional parabolic partial differential equations.
Variational convergence of nonlinear diffusion equations: applications to concentrated capacity problems with change of phase
We study a variational formulation for a Stefan problem in two adjoining bodies, when the heat conductivity of one of them becomes infinitely large. We study the «concentrated capacity» model arising in the limit, and we justify it by an asymptotic analysis, which is developed in the general framework of the abstract evolution equations of monotone type.
Variational inequalities of strongly nonlinear elliptic operators of infinite order.
Variational problems with free boundaries for the fractional Laplacian
We discuss properties (optimal regularity, nondegeneracy, smoothness of the free boundary etc.) of a variational interface problem involving the fractional Laplacian; due to the nonlocality of the Dirichlet problem, the task is nontrivial. This difficulty is bypassed by an extension formula, discovered by the first author and Silvestre, which reduces the study to that of a codimension 2 (degenerate) free boundary.
Variational problems with pointwise constraints on the derivatives.
Vectorial quasilinear diffusion equation with dynamic boundary condition
In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S) with a nonnegative constant , and for any , (S) can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain , and the parabolic equation on the boundary , having a sufficient smoothness. The objective of this study is to establish a mathematical method, which can...
Viscosity solutions and regularity of the free boundary for the limit of an elliptic two phase singular perturbation problem
Viscosity solutions of fully nonlinear functional parabolic PDE.
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...