Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method.
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.
Excess charge for pseudo-relativistic atoms in Hartree-Fock theory.
Existence and analyticity of lump solutions for generalized Benney-Luke equations.
Existence and asymptotic behaviour of standing waves for quasilinear Schrödinger–Poisson systems in
Existence and asymptotics of solutions of the Debye-Nernst-Planck system in ℝ²
We investigate a system describing electrically charged particles in the whole space ℝ². Our main goal is to describe large time behavior of solutions which start their evolution from initial data of small size. This is achieved using radially symmetric self-similar solutions.
Existence and continuous dependence results in the dynamical theory of piezoelectricity
The paper is concerned with the dynamical theory of linear piezoelectricity. First, an existence theorem is derived. Then, the continuous dependence of the solutions upon the initial data and body forces is investigated.
Existence and orbital stability of cnoidal waves for a 1D Boussinesq equation.
Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions.
Existence and regularity of the solution of a time dependent Hartree-Fock equation coupled with a classical nuclear dynamics.
We study an Helium atom (composed of one nucleus and two electrons) submitted to a general time dependent electric field, modeled by the Hartree-Fock equation, whose solution is the wave function of the electrons, coupled with the classical Newtonian dynamics, for the position of the nucleus. We prove a result of existence and regularity for the Cauchy problem, where the main ingredients are a preliminary study of the regularity in a nonlinear Schrödinger equation with semi-group techniques and...
Existence and stability of solitary waves of Boussinesq-type equations
Existence and stability of steady waves for the Hasegawa-Mima equation.
Existence and uniform boundedness of strong solutions of the time-dependent Ginzburg-Landau equations of superconductivity.
Existence and uniqueness for a nonlinear dispersive equation.
Existence and uniqueness for magnetohydrodynamic flows in pipes with viscosity dependent on the temperature.
Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems
A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.
Existence and uniqueness of a periodic solution to the two-dimensional generalized Korteweg-de Vries equation
Existence and uniqueness of global solutions to a model for the flow of an incompressible, barotropic fluid with capillary effects.
Existence and Uniqueness of Solutions for the Generalized Korteweg de Vries Equations.
Existence and uniqueness of the solution of the coupled conduction-radiation energy transfer on diffuse-gray surfaces.