Local existence and stability for a hyperbolic-elliptic system modeling two-phase reservoir flow.
Local existence of a solution of a semi-linear wave equation in a neighborhood of initial characteristic hypersurfaces
Local existence of solutions for an aggregation equation in Besov spaces
We prove the local in time existence of solutions for an aggregation equation in Besov spaces. The Fourier localization technique and Littlewood-Paley theory are the main tools used in the proof.
Local existence of solutions of the mixed problem for the system of equations of ideal relativistic hydrodynamics
Existence and uniqueness of local solutions for the initial-boundary value problem for the equations of an ideal relativistic fluid are proved. Both barotropic and nonbarotropic motions are considered. Existence for the linearized problem is shown by transforming the equations to a symmetric system and showing the existence of weak solutions; next, the appropriate regularity is obtained by applying Friedrich's mollifiers technique. Finally, existence for the nonlinear problem is proved by the method...
Local Existence of Weak Solutions to the Quasi-Linear Wave Equation for Large Initial Values.
Local generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in two independent variables
Local solution of Carrier's equation in a noncylindrical domain.
Localisation et front d'onde analytique
Logarithmic stabilization of the Kirchhoff plate transmission system with locally distributed Kelvin-Voigt damping
We are concerned with a transmission problem for the Kirchhoff plate equation where one small part of the domain is made of a viscoelastic material with the Kelvin-Voigt constitutive relation. We obtain the logarithmic stabilization result (explicit energy decay rate), as well as the wellposedness, for the transmission system. The method is based on a new Carleman estimate to obtain information on the resolvent for high frequency. The main ingredient of the proof is some careful analysis for the...
Long time behaviour of a Cahn-Hilliard system coupled with viscoelasticity
The long-time behaviour of a unique regular solution to the Cahn-Hilliard system coupled with viscoelasticity is studied. The system arises as a model of the phase separation process in a binary deformable alloy. It is proved that for a sufficiently regular initial data the trajectory of the solution converges to the ω-limit set of these data. Moreover, it is shown that every element of the ω-limit set is a solution of the corresponding stationary problem.
Long-term damped dynamics of the extensible suspension bridge.
Long-time behavior for a regularized scalar conservation law in the absence of genuine nonlinearity
Long-time behavior of nonlinear elastic waves
Long-time behavior of small solutions to quasilinear dissipative hyperbolic equations
We give sufficient conditions for the existence of global small solutions to the quasilinear dissipative hyperbolic equation corresponding to initial values and source terms of sufficiently small size, as well as of small solutions to the corresponding stationary version, i.e. the quasilinear elliptic equation We then give conditions for the convergence, as , of the solution of the evolution equation to its stationary state.
Low regularity and local well-posedness for the dimensional Dirac-Klein-Gordon system.
Low regularity solutions for Dirac-Klein-Gordon equations in one space dimension.
Low regularity solutions of the Chern-Simons-Higgs equations in the Lorentz gauge.
Low regularity well-posedness for the one-dimensional Dirac-Klein-Gordon system.
Lp - Lp'-Estimates for Fourier Integral Operators Related to Hyperbolic Equations.
Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I.