Integrated Semigroups and Integrodifferential Equations.
Integrated semigroups, C-semigroups, and the abstract Cauchy problem.
Interpolation linéaire associée à un générateur de semi-groupe intégré
Interpolation of semigroups and integrated semigroups.
Invariance of a closed convex set under a semigroup associated with a nonlinear form. (Invariance d'un convexe fermé par un semi-groupe associé à une forme non-linéaire.)
Kato-Protter type inequalities, bounded vectors and the exponential function
Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator
Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on , we define the notion of Kolmogorov kernel estimates. This allows us to show that under Dirichlet boundary conditions Ornstein-Uhlenbeck operators are generators of consistent, positive, (quasi-) contractive -semigroups on for all and for every domain . For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.
-resolvent estimates and time decay for generalized thermoelastic plate equations.
-Непрерывные селекторы неподвижных точек многозначных отображений с разложимыми значениями. III. Приложения
Laplace transform generation theorems and local Cauchy problems.
Laplace Transforms and ...-Times Integrated Semigroups.
Less than one implies zero
In this paper we show that from an estimate of the form , we can conclude that C(t) equals cos(at)I. Here is a strongly continuous cosine family on a Banach space.
Letter to the editor.
Linear and nonlinear abstract differential equations of high order
The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established....
Linear modulus of a multidimensional semigroup of -contractions and a differentiation theorem
Linear neutral partial differential equations: A semigroup approach.
Local attractivity in nonautonomous semilinear evolution equations
We study the local attractivity of mild solutions of equations in the form u’(t) = A(t)u(t) + f (t, u(t)), where A(t) are (possible) unbounded linear operators in a Banach space and where f is a (possible) nonlinear mapping. Under conditions of exponential stability of the linear part, we establish the local attractivity of various kinds of mild solutions. To obtain these results we provide several results on the Nemytskii operators on the space of the functions which converge to zero at infinity...
Local existence of the solution to the initial-boundary value problem in nonlinear thermodiffusion in micropolar medium.
Local integrated C-semigroups
We introduce the notion of a local n-times integrated C-semigroup, which unifies the classes of local C-semigroups, local integrated semigroups and local C-cosine functions. We then study its relations to the C-wellposedness of the (n + 1)-times integrated Cauchy problem and second order abstract Cauchy problem. Finally, a generation theorem for local n-times integrated C-semigroups is given.
Loss of exponential stability for a thermoelastic system with memory.