Évolution d'une onde simple pour des équations non-linéaires générales
Evolution equations governed by Lipschitz continuous non-autonomous forms
We prove -maximal regularity of the linear non-autonomous evolutionary Cauchy problem where the operator arises from a time depending sesquilinear form on a Hilbert space with constant domain We prove the maximal regularity in when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed by El-Mennaoui, Keyantuo, Laasri (2011), El-Mennaoui, Laasri (2013), and Laasri (2012). As a consequence, we obtain an invariance...
Exact controllability of a pluridimensional coupled problem.
We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn, n C [2,3], with a crack and the second one is the crack. this problem comes from Ciarlet et al. (1989), that obtained an analogous coupled problem. We show that the solution has singularities due to the crack. As in Grisvard (1989), we adapt the Hilbert uniqueness method of J.-L. Lions (1968,1988) in order to obtain the exact controllability of the associated wave equation with...
Example of an -harmonic function which is not on a dense subset.
Existence and nonexistence of classical solutions of the Dirichlet problem for a class of fully nonlinear nonuniformly elliptic equations
Existence and regularity for semilinear parabolic evolution equations
Existence and regularity of optimal solution for a dead oil isotherm problem.
Existence and Regularity of Solutions for a Semilinear First-Order Equation on the Torus.
Existence and uniqueness for a nonlinear dispersive equation.
Existence and Uniqueness of Solutions for the Generalized Korteweg de Vries Equations.
Existence for a Cauchy-Dirichlet problem for evolutional p-Laplacian systems
We study the existence of a weak solution to a Cauchy-Dirichlet problem for evolutional p-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional p-Laplacian system with an L¹-function as external force. The key ingredient is the maximum principle for weak solutions.
Existence locale de solutions pour l’équation de Monge-Ampère réelle
Existence, non-existence and regularity of radial ground states for p-laplacian equations with singular weights
Existence of C... local Solutions for the Monge-Ampère equation.
Existence of regular solutions to the stationary Navier-Stokes equations.
Existence of solutions for hyperbolic system of second order outside a domain.
Existence of solutions to a phase-field model with phase-dependent heat absorption.
Existence of solutions to -Laplace equations with logarithmic nonlinearity.
Existence of solutions to the (rot,div)-system in -weighted spaces
The existence of solutions to the elliptic problem rot v = w, div v = 0 in a bounded domain Ω ⊂ ℝ³, , S = ∂Ω in weighted -Sobolev spaces is proved. It is assumed that an axis L crosses Ω and the weight is a negative power function of the distance to the axis. The main part of the proof is devoted to examining solutions of the problem in a neighbourhood of L. The existence in Ω follows from the technique of regularization.
Existence results for quasilinear elliptic systems in .