Existence results for quasilinear elliptic systems in .
Existenz und Eindeutigkeit für Lösungen des Neumann-Tricomi-Problems im ...
Explicit exponential decay bounds in quasilinear parabolic problems.
Explicit inequalities for parabolic and pseudoparabolic equations with Neumann boundary conditions.
Exponential attractors for a Cahn-Hilliard model in bounded domains with permeable walls.
Exponential stability of solutions of the Cauchy problem for a diffusion equation with absorption with a distribution initial condition.
Extension of an integral inequality of C. Miranda and applications to the elliptic equations with discontinuous coefficients
Extinction and decay estimates of solutions for a class of porous medium equations.
Finite-dimensionality of 2-D micropolar fluid flow with periodic boundary conditions
This paper is devoted to proving the finite-dimensionality of a two-dimensional micropolar fluid flow with periodic boundary conditions. We define the notions of determining modes and nodes and estimate their number. We check how the distribution of the forces and moments through modes influences the estimate of the number of determining modes. We also estimate the dimension of the global attractor. Finally, we compare our results with analogous results for the Navier-Stokes equation.
Finitude d'espaces d'états liés pour certains systèmes quantiques
Forced vibrations in one-dimensional nonlinear thermoelasticity as a local coercive-like problem
Forced vibrations of wave equations with non-monotone nonlinearities
Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...
Free-energy-dissipative schemes for the Oldroyd-B model
In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman in [J. Non-Newtonian...
Frequency functions on the Heisenberg group, the uncertainty principle and unique continuation
A recent result of Bahouri shows that continuation from an open set fails in general for solutions of where and is a (nonelliptic) operator in satisfying Hörmander’s condition for hypoellipticity. In this paper we study the model case when is the subelliptic Laplacian on the Heisenberg group and is a zero order term which is allowed to be unbounded. We provide a sufficient condition, involving a first order differential inequality, for nontrivial solutions of to have a finite order...
Fully nonlinear second order elliptic equations with large zeroth order coefficient
We prove the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an a priori estimate asserting that the -norm of the solution cannot lie in a certain interval of the positive real axis.
Functional differential equations with non-local boundary conditions.
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
We propose a numerical analysis of proper orthogonal decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and – whereas a general uniform continuity bound seems out...
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
We propose a numerical analysis of proper orthogonal decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and – whereas a general uniform continuity bound seems out...
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
We propose a numerical analysis of proper orthogonal decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and – whereas a general uniform continuity bound seems out...