We characterize the domain of the realizations of the linear parabolic operator G defined by (1.4) in L spaces with respect to a suitable measure, that is invariant for the associated evolution semigroup. As a byproduct, we obtain optimal L 2 regularity results for evolution equations with time-depending Ornstein-Uhlenbeck operators.

We consider the heat semigroup generated by the Laplace operator on metric trees. Among our results we show how the behavior of the associated heat kernel depends on the geometry of the tree. As applications we establish new eigenvalue estimates for Schrödinger operators on metric trees.

In this paper we establish Strichartz type estimates associated with a class of semigroup operators in Rn, which for n = 2 correspond to some 2D water wave models. We also establish a nonlinear scattering result for solutions of the generalized Benney-Luke equation for higher order nonlinearity and small data initial in the energy space.

We investigate the Bi-Laplacian with Wentzell boundary conditions in a bounded domain $\Omega\subseteq\mathbb{R}^d$ Lipschitz $\Gamma$. More precisely, using form methods, we show that associated operator on ground space $L^2(\Omega)\times L^2(\Gamma)$ has compact resolvent and generates holomorphic strongly continuous real semigroup of self-adjoint operators. Furthermore, give full characteriz...

We present a spectral mapping theorem for semigroups on any Banach space E. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for £-valued functions. This characterization is given in terms of the spectrum of the generator of the semigroup of evolutionary operators.

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with impulses in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. ifx

In this paper, stability analysis and periodic optimal control problems for a class of an impulsive periodic system in Banach spaces is considered. Combining exponential stabilizability and impulsive evolution operators, we present the existence of periodic optimal controls without assuming the semigroup is compact or exponentially stable. Finally, an example is given for demonstration. AMS sub...

In this paper we investigate a class of nonautonomous linear parabolic problems with time-depending Ornstein-Uhlenbeck operators. We study the asymptotic behavior of the associated evolution operator and evolution semigroup in the periodic and non-periodic situation. Moreover, we show that the associated evolution operator is hypercontractive.

We present c0–semigroup generation results for the free streaming operator with abstract boundary conditions. We recall some known results on the matter and establish a general theorem (already announced in [1]). We motivate our study with a lot of examples and show that our result applies to the physical cases of Maxwell boundary conditions in the kinetic theory of gases as well as to the non—...

Let S be a locally compact foundation semigroup with identity and                          be its semigroup algebra. Let X be a weak*-closed left translation invariant subspace of    In this paper, we prove that  X  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. We also prove that a foundation semigroup with identity S is left amenab...