Analytic Singularities and Microhyperbolic Boundary Value Problems.
Analyticity and smoothing effect for the Schrödinger equation
Anisotropic inverse problems and Carleman estimates
This note reports on recent results on the anisotropic Calderón problem obtained in a joint work with Carlos E. Kenig, Mikko Salo and Gunther Uhlmann [8]. The approach is based on the construction of complex geometrical optics solutions to the Schrödinger equation involving phases introduced in the work [12] of Kenig, Sjöstrand and Uhlmann in the isotropic setting. We characterize those manifolds where the construction is possible, and give applications to uniqueness for the corresponding anisotropic...
Anisotropic parabolic equations with variable nonlinearity.
Application of Rothe's method to perturbed linear hyperbolic equations and variational inequalities
Approximation des systèmes d'opérateurs pseudodifférentiels
Approximation of a nonlinear thermoelastic problem with a moving boundary via a fixed-domain method
The thermoelastic stresses created in a solid phase domain in the course of solidification of a molten ingot are investigated. A nonlinear behaviour of the solid phase is admitted, too. This problem, obtained from a real situation by many simplifications, contains a moving boundary between the solid and the liquid phase domains. To make the usage of standard numerical packages possible, we propose here a fixed-domain approximation by means of including the liquid phase domain into the problem (in...
A-Priori Schranken für Lösungen gewisser elliptischer Probleme.
A-priori-Schranken für semi- und quasilineare parabolische Differentialgleichungen.
Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity
We show that the critical nonlinear elliptic Neumann problem in , in , on , where is a bounded and smooth domain in , has arbitrarily many solutions, provided that is small enough. More precisely, for any positive integer , there exists such that for , the above problem has a nontrivial solution which blows up at interior points in , as . The location of the blow-up points is related to the domain geometry. The solutions are obtained as critical points of some finite-dimensional...
Asymptotic behavior of a periodic diffusion system.
Asymptotic behavior of solutions to a reaction-diffusion system with a cross diffusion matrix on unbounded domains.
Asymptotic behavior of the solution of quasilinear parametric variational inequalities in a beam with a thin neck.
Asymptotic behaviour of the porous media equation in an exterior domain
Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem
Asymptotic estimates for a perturbation of the linearization of an equation for compressible viscous fluid flow
We prove a priori estimates for a linear system of partial differential equations originating from the equations for the flow of a barotropic compressible viscous fluid under the influence of the gravity it generates. These estimates will be used in a forthcoming paper to prove the nonlinear stability of the motionless, spherically symmetric equilibrium states of barotropic, self-gravitating viscous fluids with respect to perturbations of zero total angular momentum. These equilibrium states as...
Asymptotic estimates in Weighted Hölder spaces for a class of elliptic scale-covariant second order operators
Asymptotic expansions for linear symmetric hyperbolic systems with small parameter.
Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows
Asymptotics for quasilinear elliptic non-positone problems
In the recent years, many results have been established on positive solutions for boundary value problems of the form in Ω, u(x)=0 on ∂Ω, where λ > 0, Ω is a bounded smooth domain and f(s) ≥ 0 for s ≥ 0. In this paper, a priori estimates of positive radial solutions are presented when N > p > 1, Ω is an N-ball or an annulus and f ∈ C¹(0,∞) ∪ C⁰([0,∞)) with f(0) < 0 (non-positone).