Linear differential Equations in Two Variables of Rank Four. I.
Linear-quadratic optimal control for the Oseen equations with stabilized finite elements
For robust discretizations of the Navier-Stokes equations with small viscosity, standard Galerkin schemes have to be augmented by stabilization terms due to the indefinite convective terms and due to a possible lost of a discrete inf-sup condition. For optimal control problems for fluids such stabilization have in general an undesired effect in the sense that optimization and discretization do not commute. This is the case for the combination of streamline upwind Petrov-Galerkin (SUPG) and pressure...
Liouville type theorem for solutions of linear partial differential equations with constant coefficients
We discuss existence of global solutions of moderate growth to a linear partial differential equation with constant coefficients whose total symbol P(ξ) has the origin as its only real zero. It is well known that for such equations, global solutions tempered in the sense of Schwartz reduce to polynomials. This is a generalization of the classical Liouville theorem in the theory of functions. In our former work we showed that for infra-exponential growth the corresponding assertion is true if and...
Liouville-Gelfand type problems for the -laplacian on bounded domains of
Lipschitz Continuous Solutions for Nonlinear Obstacle Problems.
Littlewood-paley decomposition associated with the dunkl operators and paraproduct operators.
lnfinitely many solutions for fractional Schrödinger equations with perturbation via variational methods
Using variational methods, we investigate the solutions of a class of fractional Schrödinger equations with perturbation. The existence criteria of infinitely many solutions are established by symmetric mountain pass theorem, which extend the results in the related study. An example is also given to illustrate our results.
Local existence of classical solutions to the well-posed Hele-Shaw problem.
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 Weak Solutions to the Quasi-Linear Wave Equation for Large Initial Values.
Local free boundary problem for incompressible magnetohydrodynamics [Book]
Local solvability for semilinear partial differential equations of constant strength.
Local solvability of some classes of linear and nonlinear partial differential equations.
Local-in-time existence for the non-resistive incompressible magneto-micropolar fluids
We establish the local-in-time existence of a solution to the non-resistive magneto-micropolar fluids with the initial data , and for and any . The initial regularity of the micro-rotational velocity is weaker than velocity of the fluid .
Localisation et front d'onde analytique
Localizations of partial differential operators and surjectivity on real analytic functions
Let P(D) be a partial differential operator with constant coefficients which is surjective on the space A(Ω) of real analytic functions on an open set . Then P(D) admits shifted (generalized) elementary solutions which are real analytic on an arbitrary relatively compact open set ω ⊂ ⊂ Ω. This implies that any localization of the principal part is hyperbolic w.r.t. any normal vector N of ∂Ω which is noncharacteristic for . Under additional assumptions must be locally hyperbolic.
Long-Range and Periodic Solutions of Parabolic Problems.
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.
L’opérateur de Casimir de
Lösung der Dirichletproblems und Konvergenz der Differenzenapproximation für elliptische Differentialgleichungen zweiter Ordnung.