A variational approach for a semi-linear parabolic equation with measure data
A variational method for parameter identification
A variational treatment for general elliptic equations of the flame propagation type : regularity of the free boundary
A waiting time phenomenon for thin film equations
A wavelet Galerkin method applied to partial differential equations with variable coefficients.
About asymptotic and oscillation properties of the Dirichlet problem for delay partial differential equations.
About existence and uniqueness of the restricted total least squares estimation.
About mathematical models of phase transitions.
About stability and regularization of ill-posed elliptic Cauchy problems: the case of C1,1 domains
This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace's equation in domains with C1,1 boundary. It is an extension of an earlier result of [Phung, ESAIM: COCV9 (2003) 621–635] for domains of class C∞. Our estimate is established by using a Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Furthermore, we prove that this stability estimate is nearly optimal and induces...
About the interface of some nonlinear diffusion problems.
Abrupt and smooth separation of free boundaries in flow problems
Absence of global solutions to a class of nonlinear parabolic inequalities
We study the absence of nonnegative global solutions to parabolic inequalities of the type , where , 0 < β ≤ 2, is the β/2 fractional power of the Laplacian. We give a sufficient condition which implies that the only global solution is trivial if p > 1 is small. Among other properties, we derive a necessary condition for the existence of local and global nonnegative solutions to the above problem for the function V satisfying , where a ≥ 0, b > 0, p > 1 and V₊(x): = maxV(x),0. We...
Absence of solutions to higher-order evolution differential inequalities.
Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs
Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize...
Actions on environment under uncertainty: stochastic formulation and the associated deterministic problem.
Adapting meshes and time-steps for phase change problems
We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.
Adaptive fast marching and level set methods for propagating interfaces.
Adiabatic Evolution of Coupled Waves for a Schrödinger-Korteweg-de Vries System
The effective dynamics of interacting waves for coupled Schrödinger-Korteweg-de Vries equations over a slowly varying random bottom is rigorously studied. One motivation for studying such a system is better understanding the unidirectional motion of interacting surface and internal waves for a fluid system that is formed of two immiscible layers. It was shown recently by Craig-Guyenne-Sulem [1] that in the regime where the internal wave has a large...
Aggregation on a nonlinear parabolic functional differential equation.
Algèbres différentielles et problème de Goursat non linéaire à données irrégulières