Relaxation approximations and bounded variation estimates for some partial differential equations.
Relaxations semi-linéaire et cinétique des systèmes de lois de conservation
Remark on periodic solutions of a linear wave equation in one dimension
Remark on the null-condition for the nonlinear wave equation
Dimostriamo l'esistenza della soluzione globale per un sistema di equazioni delle onde con nonlinearità quadratica dipendente dalle variabili spazio-tempo. Come in [3] la tecnica è basata sulla trasformazione di Penrose.
Remark to dynamic contact problems for bodies with a singular memory
The existence of a solution to the dynamic contact of a body having a singular memory with a rigid undeformable support is proved under some weaker assumption than that in [3].
Remark to the comparison of solution properties of Love's equation with those of wave equation
In the paper some solution properties of the Love's equation are compared with those of the classical wave equation for a certain class of boundary conditions. The method of small parameter is used.
Remarks on bounded solutions of a semilinear dissipative hyperbolic equation
Remarks on Carleman estimates and exact controllability of the Lamé system
In this paper we established the Carleman estimate for the two dimensional Lamé system with the zero Dirichlet boundary conditions. Using this estimate we proved the exact controllability result for the Lamé system with with a control locally distributed over a subdomain which satisfies to a certain type of nontrapping conditions.
Remarks on nonlinear biharmonic evolution equation of Kirchhoff type in noncylindrical domain.
Remarks on quasilinear evolutions equations.
Remarks on the existence an uniqueness of global decaying solutions of the nonlinear dissipative wave equations.
Remarks on the existence and decay of the nonlinear beam equation.
Remarks on the Klein-Gordon equation
Remarks on the qualitative behavior of the undamped Klein-Gordon equation
We present sufficient conditions on the initial data of an undamped Klein-Gordon equation in bounded domains with homogeneous Dirichlet boundary conditions to guarantee the blow up of weak solutions. Our methodology is extended to a class of evolution equations of second order in time. As an example, we consider a generalized Boussinesq equation. Our result is based on a careful analysis of a differential inequality. We compare our results with the ones in the literature.
Remarks on the wave equation with a nonlinear term with respect to the velocity
Remarks on vacuum state and uniqueness of concentration process.
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble....
Remarks on weak stabilization of semilinear wave equations
If a second order semilinear conservative equation with esssentially oscillatory solutions such as the wave equation is perturbed by a possibly non monotone damping term which is effective in a non negligible sub-region for at least one sign of the velocity, all solutions of the perturbed system converge weakly to 0 as time tends to infinity. We present here a simple and natural method of proof of this kind of property, implying as a consequence some recent very general results of Judith Vancostenoble. ...
Remarque sur «R. G. McLenaghan : on the validity of Huygens principle for second order partial differential equations with four independent variables. I»
Remarques sur la caractérisation des problèmes mixtes bien posés pour un opérateur hyperbolique