Strong instability of solitary waves for nonlinear Klein–Gordon equations and generalized Boussinesq equations
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...
We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.
A solution of a particular Dirichlet problem for a non-linear 2nd order hyperbolic equation is regular at any point of the boundary but one point. The kind of singularity which exhibits at this point is investigated.
In this paper we study boundary value problems for first order partial differential equations on sets of finite perimeter in the sense of De Giorgi (see [7]). We also study a new type of boundary value problems which has been suggested by issues about the bounce problem.
Pour un système parabolique de lois de conservation, nous considérons le problème mixte, dans le domaine . Pour une condition de Dirichlet, le système admet en général des solutions stationnaires , qui tendent vers une limite en . Ce sont les profils des couches limites, dans l’approximation du second ordre, pour le système hyperbolique du premier ordre sous-jacent. La stabilité de cette couche limite est liée à la stabilité linéaire asymptotique de . On étudie celle-ci au moyen d’une fonction d’Evans,...