Attractors of asymptotically periodic multivalued dynamical systems governed by time-dependent subdifferentials.
Attractors of multivalued semiflows generated by differential inclusions and their approximations.
Bi-spaces global attractors in abstract parabolic equations
An abstract semilinear parabolic equation in a Banach space X is considered. Under general assumptions on nonlinearity this problem is shown to generate a bounded dissipative semigroup on . This semigroup possesses an -global attractor that is closed, bounded, invariant in , and attracts bounded subsets of in a ’weaker’ topology of an auxiliary Banach space Z. The abstract approach is finally applied to the scalar parabolic equation in Rⁿ and to the partly dissipative system.
Bounded and periodic solutions of semilinear impulsive periodic system on Banach spaces.
Cauchy problems with periodic controls.
Coercive solvability of the nonlocal boundary value problem for parabolic differential equations.
Corrigendum to Maximal regularity and Hardy spaces.
Energy error estimates for the projection-difference method with the Crank--Nicolson scheme for parabolic equations.
Evolution equations governed by Lipschitz continuous non-autonomous forms
We prove -maximal regularity of the linear non-autonomous evolutionary Cauchy problem where the operator arises from a time depending sesquilinear form on a Hilbert space with constant domain We prove the maximal regularity in when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed by El-Mennaoui, Keyantuo, Laasri (2011), El-Mennaoui, Laasri (2013), and Laasri (2012). As a consequence, we obtain an invariance...
Existence and analyticity of a parabolic evolution operator for nonautonomous linear equations in Banach spaces.
Existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions and its applications
We establish the existence of solutions for evolution equations in Hilbert spaces with anti-periodic boundary conditions. The energies associated to these evolution equations are quadratic forms. Our approach is based on application of the Schaefer fixed-point theorem combined with the continuity method.
Existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces with anti-periodic boundary conditions
The paper is devoted to the study of the existence of solutions for nonlinear nonmonotone evolution equations in Banach spaces involving anti-periodic boundary conditions. Our approach in this study relies on the theory of monotone and maximal monotone operators combined with the Schaefer fixed-point theorem and the monotonicity method. We apply our abstract results in order to solve a diffusion equation of Kirchhoff type involving the Dirichlet -Laplace operator.
Existence of solutions to quasilinear functional differential equations.
Existence results for a class of semi-linear evolution equations.
Exponentially convergent parallel discretization methods for the first order evolution equations.
High-degree precision decomposition method for an evolution problem.
Linear parabolic problems involving measures.
Desarrollamos una teoría general para la resolución de ecuaciones lineales de evolución de la forma ü + Au = μ sobre R+, donde -A es el generador infinitesimal de un semigrupo analítico fuertemente continuo y μ es una medida de Radón con valores en un espacio de Banach. Utilizamos la teoría de interpolación-extrapolación de espacios y el teorema de representación de Riesz para tales medidas.Los resultados abstractos son ilustrados mediante aplicaciones a problemas de valor inicial parabólicos de...
Maximal regularity and Hardy spaces
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in -spaces
Several abstract model problems of elliptic and parabolic type with inhomogeneous initial and boundary data are discussed. By means of a variant of the Dore-Venni theorem, real and complex interpolation, and trace theorems, optimal -regularity is shown. By means of this purely operator theoretic approach, classical results on -regularity of the diffusion equation with inhomogeneous Dirichlet or Neumann or Robin condition are recovered. An application to a dynamic boundary value problem with surface...