Related papers: Evolutionary integro-differential equations of sca…
We prove existence, uniqueness and give the analytical solution of heat and wave type equations on a compact Lie group $G$ by using a non-local (in time) differential operator and a positive left invariant operator (maybe unbounded) acting…
This paper is devoted to the study of generalised time-fractional evolution equations involving Caputo type derivatives. Using analytical methods and probabilistic arguments we obtain well-posedness results and stochastic representations…
We consider a general class of integro-differential evolution equations which includes the governing equation of the generalized grey Brownian motion and the time- and space-fractional heat equation. We present a general relation between…
We prove a compactness result related to $G$-convergence for autonomous evolutionary equations in the sense of Picard. Compared to previous work related to applications, we do not require any boundedness or regularity of the underlying…
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…
We survey methods and results of fractional differential equations in which an unknown function is under the operation of integration and/or differentiation of fractional order. As an illustrative example, we review results on fractional…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
Let $G$ be a compact Lie group. In this article, we consider the initial value fractional wave equation with power-type nonlinearity on $G$. Mainly, we investigate some $L^{2}-L^{2}$ estimates of the solutions to the homogeneous fractional…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of…
We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is on the asymptotic behaviour and positivity properties of…
We study a nonlinear integro-differential equation arising in population dynamics. It has been already proved by Rybka, Tang and Waxman that it has a unique local in time solution. Here, after deriving appropriate a priori estimates we show…
A well-posedness result for a time-shift invariant class of evolutionary operator equations involving material laws with fractional time-integrals of order $\alpha\in]0,1[$ is considered and exemplified by an application to a Kelvin-Voigt…
In this paper we prove the local and global well-posedness of the time fractional abstract Schr\"odinger type evolution equation on the Hilbert space and as an application, we prove the local and global well-posedness of the fractional…
We study quasilinear evolutionary partial integro-differential equations of second order which include time fractional $p$-Laplace equations of time order less than one. By means of suitable energy estimates and De Giorgi's iteration…
Strichartz estimates are a manifestation of a dispersion phenomenon, exhibited by certain partial differential equations, which is detected by suitable Lebesgue space norms. In most cases the evolution propagator $U(t)$ is a one parameter…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
In this paper, we deal with the initial value fractional damped wave equation on $G$, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we…
This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoelliptic operators, with homogeneous multi-point time-nonlocal…
In this paper, we study quantitative spatial analytic bounds and unique continuation inequalities of solutions for fractional heat equations with an analytic lower order term on the whole space. At first, we show that the solution has a…