Linearized stability results in continuous interpolation spaces
Local and global solutions of well-posed integrated Cauchy problems
We study the local well-posed integrated Cauchy problem , v(0) = 0, t ∈ [0,κ), with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.
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 ergodic properties of -operator semigroups
Local existence of the solution to the initial-boundary value problem in nonlinear thermodiffusion in micropolar medium.
Local existence, uniqueness and regularity for a class of degenerate parabolic systems arising in biological models
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.
Locally Lipschitz continuous integrated semigroups
This paper is concerned with the problem of real characterization of locally Lipschitz continuous (n + 1)-times integrated semigroups, where n is a nonnegative integer. It is shown that a linear operator is the generator of such an integrated semigroup if and only if it is closed, its resolvent set contains all sufficiently large real numbers, and a stability condition in the spirit of the finite difference approximation theory is satisfied.
Logarithmic Sobolev inequalities for inhomogeneous Markov Semigroups
We investigate the dissipativity properties of a class of scalar second order parabolic partial differential equations with time-dependent coefficients. We provide explicit condition on the drift term which ensure that the relative entropy of one particular orbit with respect to some other one decreases to zero. The decay rate is obtained explicitly by the use of a Sobolev logarithmic inequality for the associated semigroup, which is derived by an adaptation of Bakry's Γ-calculus. As a byproduct,...
Logarithmic Sobolev inequalities for unbounded spin systems revisited
Long-Time Asymptotic Properties of Dynamical Semigroups on W*-algebras.
Loss of exponential stability for a thermoelastic system with memory.
Lototsky-Schnabl Operators Associated with a Strictly Elliptic Differential Operator and Their Corresponding Feller Semigroup.
Lototsky-Schnabl Operators on Compact Convex Sets and Their Associated Limit Semigroups.
Lower bounds on //K...//1...... For some contractions K of L² (...), with applications to Markov operators.