Related papers: Semigroups generated in Lp-spaces by some dispersa…
Ranges of the real-valued parameters $\alpha$, $a$, $b$, and $m$ are identified for which the operator $$\mathcal{A}_{\alpha}(a,b)f(x):=x^\alpha\left(f''(x)+\frac{a}{x}f'(x)+\frac{b}{x^2}f(x)\right), \quad x>0,$$ generates an analytic…
We develop and implement new probabilistic strategy for proving basic results about long time behaviour for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process as…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
We consider a class of vector-valued elliptic operators with unbounded coefficients, coupled up to the first-order, in the Lebesgue space L^p(R^d;R^m) with p in (1,\infty). Sufficient conditions to prove generation results of an analytic…
This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a…
In this paper we analyse a class of nonlinear cross-diffusion systems for two species with local repulsive interactions that exhibit a formal gradient flow structure with respect to the Wasserstein metric. We show that systems where the…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We prove well-posedness for very general linear wave- and diffusion equations on compact or non-compact metric graphs allowing various different conditions in the vertices. More precisely, using the theory of strongly continuous operator…
Let $\mathcal{X}$ be a real separable Hilbert space. Let $C$ be a linear, bounded and positive operator on $\mathcal{X}$ and let $A$ be the infinitesimal generator of a strongly continuous semigroup on $\mathcal{X}$. Let $\{W(t)\}_{t\geq…
In this work, we develop a new biological transmission model for Chagas disease. This model, set in two juxtaposed habitats with skew Brownian motion conditions at the interface, is composed of two reaction--diffusion equations and takes…
Motivated by the recent developments of pseudo-hermitian quantum mechanics, we analyze the structure of unbounded metric operators in a Hilbert space. It turns out that such operators generate a canonical lattice of Hilbert spaces, that is,…
We develop a new semi-analytical method for solving multilayer diffusion problems with time-varying external boundary conditions and general internal boundary conditions at the interfaces between adjacent layers. The convergence rate of the…
We consider two systems of two conservation laws that are defined on complementary, one-dimensional spatial intervals and coupled by an interface as a single port-Hamiltonian system. In case of a fixed interface position, we characterize…
In this work we investigate the well-posedness for difussion equations associated to subelliptic pseudo-differential operators on compact Lie groups. The diffusion by strongly elliptic operators is considered as a special case and in…
Let $\mathcal{X}$ be a real separable Hilbert space. Let $Q$ be a linear, self-adjoint, positive, trace class operator on $\mathcal{X}$, let $F:\mathcal{X}\rightarrow\mathcal{X}$ be a (smooth enough) function and let $\{W(t)\}_{t\geq 0}$ be…
We present a generation theorem for positive semigroups on an $L^1$ space. It provides sufficient conditions for the existence of positive and integrable solutions of initial-boundary value problems. An application to a two-phase cell cycle…
In this paper we prove that, under suitable assumptions on {\alpha} > 0, the operator L = (1 + |x|{\alpha})\Delta admits realizations generating contraction or analytic semigroups in Lp (RN). For some values of {\alpha}, we also explicitly…
We present several results on smoothness in $L_{p}$ sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
We propose a general model to study the interplay between spatial dispersal and environment spatiotemporal fluctuations in metapopulation dynamics. An ecological landscape of favorable patches is generated like a L\'{e}vy dust, which allows…