Absorption semigroups and Dirichlet boundary conditions.
Abstract evolution equations on variable domains : an approach by minimizing movements
Abstract methods in differential equations.
This is an expanded version, enriched by references, of my inaugural speech held on November 7, 2001 at the Real Academia de Ciencas Exactas, Físicas y Naturales in Madrid. It explains in a nontechnical way, accessible to a general scientific community, some of the motivation and basic ideas of my research of the last twenty years on a functional-analytical approach to nonlinear parabolic problems.
Abstract parabolic problem with non-Lipschitz nonlinearity
An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
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...
Abstract parabolic problems with non-Lipschitz critical nonlinearities
The Cauchy problem for a semilinear abstract parabolic equation is considered in a fractional power scale associated with a sectorial operator appearing in the linear main part of the equation. Existence of local solutions is proved for non-Lipschitz nonlinearities satisfying a certain critical growth condition.
Abstract Quasilinear Parabolic Equations.
Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs
Recently, we established some generalizations of the theory of Lagrange multipliers arising from nonlinear programming in Banach spaces, which enable us to treat not only elliptic problems but also parabolic problems in the same generalized framework. The main objective of the present paper is to discuss a typical time-dependent double obstacle problem as a new application of the above mentioned generalization. Actually, we describe it as a usual parabolic variational inequality and then characterize...
Accurate solution estimates for nonlinear nonautonomous vector difference equations.
Adapting meshes and time-steps for phase change problems
We address the numerical approximation of the two-phase Stefan problem and discuss an adaptive finite element method based on rigorous a posteriori error estimation and refinement/coarsening. We also investigate how to restrict coarsening for the resulting method to be stable and convergent. We review implementation issues associated with bisection and conclude with simulations of a persistent corner singularity, for which adaptivity is an essential tool.
Adaptive step-size control in simulation of diffusive CVD processes.
Addendum to "Hölder estimates for nonlinear degenerate parabolic systems".
Addendum to the paper “Finite element solution of quasistationary nonlinear magnetic field”
Additive Schwarz algorithms for parabolic convection-diffusion equations.
Aggregation on a nonlinear parabolic functional differential equation.
Aleksandrov-type estimates for a parabolic Monge-Ampère equation.
Almost automorphy of semilinear parabolic evolution equations.
Almost periodic solutions to systems of parabolic equations.
Almost periodic viscosity solutions of nonlinear parabolic equations.
Alternating direction Galerkin method with capacitance matrix for the parabolic problem with natural boundary condition