A parabolic analogue of Finn's maximum principle.
A Phragmén - Lindelöf Principle for Subsolutions of Quasi - Linear Equations.
A qualitative study on a parabolic free boundary problem.
A qualitative theory for parabolic problems under dynamical boundary conditions.
A rapid convergence method for a singular perturbation problem
A remark on parabolic equations.
A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence
The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system where . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L2-subcritical σ (that is σ ≤ 2/3) and the H1-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the norm.
A smoothing property for the -critical NLS equations and an application to blowup theory
A survey of results on nonlinear Venttsel problems
We review the recent results for boundary value problems with boundary conditions given by second-order integral-differential operators. Particular attention has been paid to nonlinear problems (without integral terms in the boundary conditions) for elliptic and parabolic equations. For these problems we formulate some statements concerning a priori estimates and the existence theorems in Sobolev and Hölder spaces.
A very singular solution for the dual porous medium equation and the asymptotic behaviour of general solutions.
A wave equation associated with mixed nonhomogeneous conditions: The compactness and connectivity of weak solution set.
A weighted isoperimetric inequality and applications to symmetrization.
A weighted symmetrization for nonlinear elliptic and parabolic equations in inhomogeneous media
In the theory of elliptic equations, the technique of Schwarz symmetrization is one of the tools used to obtain a priori bounds for classical and weak solutions in terms of general information on the data. A basic result says that, in the absence of lower-order terms, the symmetric rearrangement of the solution of an elliptic equation, that we write , can be compared pointwise with the solution of the symmetrized problem. The main question we address here is the modification of the method to...
About asymptotic and oscillation properties of the Dirichlet problem for delay partial differential equations.
Abschätzung nach unten für Lösungen nichtlinearer Differentialungleichungen
Abstract linear hyperbolic equations and asymptotic equivalence as
Abstract parabolic problems in ordered Banach spaces
We consider abstract parabolic problems in ordered Banach spaces and give conditions under which they have global attractors. Our approach is via comparison of solutions. Within this approach abstract comparison principles are obtained and bounds on the attractors are given by order intervals in Banach spaces. These results are applied to ordinary differential equations and to parabolic equations for which the main part is given by a sum of fractional powers of sectorial operators having increasing...
An Elementary Partial Regularity Proof for Vector-Valued Obstacle Problems.
An elementary proof for one-dimensionality of travelling waves in cylinders.
An existence result for a free boundary problem for the -Laplace operator.