Exact solutions of the generalized Benjamin-Bona-Mahony equation.
Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method.
Exact solutions to some external mixed problems in potential theory
A new and elegant procedure is proposed for the solution of mixed potential problems in a half-space with a circular line of division of boundary conditions. The approach is based on a new type of integral operators with special properties. Two general external problems are solved; i) An arbitrary potential is specified at the boundary outside a circle, and its normal derivative is zero inside; ii) An arbitrary normal derivative is given outside the circle, and be potential is zero inside. Several...
Exact solutions to some nonlinear PDEs, travelling profiles method.
Exact subelliptic estimates for n - 1 forms.
Exact traveling wave solutions for discrete conservation laws.
Example of an -harmonic function which is not on a dense subset.
Example of solving of the boundary value problems for one partial differential equations with two unknown functions
Examples of discontinuous, divergence-free solutions to elliptic variational problems
We give an example of a bounded discontinuous divergence-free solution of a linear elliptic system with measurable bounded coefficients in and a corresponding example for a Stokes-like system.
Examples of non-local time dependent or parabolic Dirichlet spaces
In [23] M. Pierre introduced parabolic Dirichlet spaces. Such spaces are obtained by considering certain families of Dirichlet forms. He developed a rather far-reaching and general potential theory for these spaces. In particular, he introduced associated capacities and investigated the notion of related quasi-continuous functions. However, the only examples given by M. Pierre in [23] (see also [22]) are Dirichlet forms arising from strongly parabolic differential operators of second order. To...
Exceptional sets for solutions to quasilinear parabolic equations in weighted Sobolev spaces.
Excess charge for pseudo-relativistic atoms in Hartree-Fock theory.
Excitation of shear waves in a piezoceramic medium with partially electrodized tunnel openings strengthened by a rigid stringer.
Exemples d’instabilités pour des équations d’ondes non linéaires
Le but de l’exposé est de donner un guide de lecture pour un article de Gilles Lebeau où il est montré que le problème de Cauchy pour l’équation d’onde surcritique est mal posé au sens de Hadamard dans l’espace d’énergie, pour en dimension 3. La preuve repose sur des constructions d’optique géométrique et des analyses d’instabilité dans des régimes fortement non linéaires. On donnera les étapes de l’analyse en essayant de les situer dans leur contexte plus général : construction de solutions...
Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in Banach spaces.
Existence and analyticity of lump solutions for generalized Benney-Luke equations.
Existence and Approximation of Solutions of Non-Linear Elliptic Equations.
Existence and approximation results for gradient flows
This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space
Existence and asymptotic behavior of boundary blow-up solutions for weighted -Laplacian equations with exponential nonlinearities.
Existence and asymptotic behavior of global solutions for a class of nonlinear higher-order wave equation.