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.
Lösung des Dirichlet Problems bei Jordangebieten mit analytischem Rand durch Interpolation.
Lp regularity of the Dirichlet problem for elliptic equations with singular drift.