Related papers: Semigroups generated in Lp-spaces by some dispersa…
We consider five different abstract Cauchy problems where the operator is of fourth order. For each problem, using semigroups techniques and functional calculus, we study the invertibility and the spectral properties of the fourth order…
Using techniques of the theory of semigroups of linear operators we study the question of approximating solutions to equations governing diffusion in thin layers separated by a semi-permeable membrane. We show that as thickness of the…
We study a transmission problem, in population dynamics, between two juxtaposed habitats. In each habitat, we consider a generalized diffusion equation composed by the Laplace operator and a biharmonic term. We consider that the…
We give sufficient conditions on an operator space $E$ and on a semigroup of operators on a von Neumann algebra $M$ to obtain a bounded analytic or a $R$-analytic semigroup $(T_t \otimes Id_E)_{t \geq 0}$ on the vector valued noncommutative…
A class of vector-valued elliptic operators with unbounded coefficients, coupled up to the second-order is investigated in the Lebesgue space $L^p(\mathbb R^d;\mathbb R^m)$ with $p \in (1,\infty)$, providing sufficient conditions for the…
The following version of the Lumer-Phillips is proved: a surjective dissipative operator is m-dissipative and invertible. The result remains true if dissipative linear relations (i.e multivalued operators) are considered. The main purpose…
The linear semigroup associated with age-structured diffusive populations is investigated in the $L_1$-setting. A complete determination of its generator is given along with detailed spectral information that imply, in particular, an…
Given a bounded domain in the Euclidean space satisfying the uniform outer cone condition, we show that a uniformly elliptic operator of second order with continuous second order coefficients generates a holomorphic semigroup on the space…
In this article, we study strictly elliptic, second-order differential operators on a bounded Lipschitz domain in $\mathbb{R}^d$, subject to certain non-local Wentzell-Robin boundary conditions. We prove that such operators generate…
We provide quantitative estimates in total variation distance for positive semi-groups, which can be non-conservative and non-homogeneous. The techniques relies on a family of conservative semigroups that describes a typical particle and…
We consider the linear thermoelastic plate equations with free boundary conditions in uniform $C^4$-domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic…
In a separable Hilbert space, we study supercontractivity and ultracontractivity properties for a transition semigroups associated with a stochastic partial differential equations. This is done in terms of exponential integrability of…
We study dispersive mixed-order systems of pseudodifferential operators in the setting of $L^p$-Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators generate a semigroup in the space of tempered distributions.…
We study diffusion and wave equations in networks. Combining semigroup and variational methods we obtain well-posedness and many nice properties of the solutions in general L^p -context. Following earlier articles of other authors, we…
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…
We study the existence of Feller semigroups arising in the theory of multidimensional diffusion processes. We study bounded perturbations of elliptic operators with boundary conditions containing an integral over the closure of the domain…
We study a system of fully nonlinear elliptic equations, depending on a small parameter $\eps$, that models long-range segregation of populations. The diffusion is governed by the negative Pucci operator. In the linear case, this system was…
We study $L^p$-theory of second-order elliptic divergence type operators with complex measurable coefficients. The major aspect is that we allow complex coefficients in the main part of the operator, too. We investigate generation of…
In this work we study, by a semigroup approach, a transmission problem based on biharmonic equations with boundary and transmission conditions, in two juxtaposed habitats. We give a result of existence and uniqueness of the classical…
This paper focuses on systems of strongly coupled elliptic operators whose coefficients may be unbounded and are defined on a domain $\Omega \subseteq \mathbb{R}^d$. It is shown that a quasi-contractive semigroup in $L^p$-spaces can be…