Existence and regularity for a minimum problem with free boundary.
Existence and regularity for semilinear parabolic evolution equations
Existence and regularity of a global attractor for doubly nonlinear parabolic equations.
Existence and regularity of entropy solutions for some nonlinear elliptic equations.
Existence and regularity of local solutions to partial neutral functional-differential equations with infinite delay.
Existence and regularity of optimal solution for a dead oil isotherm problem.
Existence and regularity of positive solutions for an elliptic system.
Existence and Regularity of Solutions for a Semilinear First-Order Equation on the Torus.
Existence and regularity of solutions of a phase field model for solidification with convection of pure materials in two dimensions.
Existence and regularity of solutions of some elliptic system in domains with edges [Book]
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 regularity of weak solutions to the Dirichletproblem for semilinear elliptic systems of higher order.
Existence and regularity of weak solutions to the prescribed mean curvature equation for a nonparametric surface.
Existence and regularity results for the gradient flow for -harmonic maps.
Existence and smoothness of solutions to second initial boundary value problems for Schrödinger systems in cylinders with non-smooth bases.
Existence and stability of asymptotically oscillatory double pulses.
Existence and stability of periodic solutions for a nonlocal evolution population problem.
The theory of maximal monotone operators is applied to prove the existence of weak periodic solutions for a nonlinear nonlocal problem. The stability of these solutions is a consequence of the Lipschitz continuous assumption on the diffusivity matrix and the death rate.
Existence and stability of solitary waves of Boussinesq-type equations
Existence and stability of steady waves for the Hasegawa-Mima equation.
Existence and stability theorems for abstract parabolic equations, and some of their applications
For a class of semi-abstract evolution equations for sections on vector bundles on a three-dimensional compact manifold we prove that for initial values with certain symmetries strong solutions exist for all times. In case these solutions become small after some time, strong solutions exist also for small perturbations of these initial values. Many systems from fluid mechanics are included in this class.