Related papers: Nonlocal and multipoint boundary value problems fo…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example,…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
This paper investigates a nonlocal boundary value problem for a multi-parametric integral-differential equation involving the Caputo-Prabhakar type operator in a bounded rectangular domain. The nonlocal conditions are given as partial…
This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow…
We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…
We discuss a semi-discrete analogue of the Unified Transform Method, introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equations of constant coefficients. The semi-discrete method…
A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot - or, in some cases, only -- periodic solutions. Several examples (ODEs and PDEs) are exhibited.
Estimates on the asymptotic behaviour of solution to linear integro-differential equations are fundamental in understanding the dynamics occuring in many nonlocal evolution problems. They are usually derived by using precise decay estimates…
Usually Fokker-Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we…
We study a semidiscrete analogue of the Unified Transform Method introduced by A. S. Fokas, to solve initial-boundary-value problems for linear evolution partial differential equations with constant coefficients on the finite interval $x…
We study elliptic equations of order $2m$ with nonlocal boundary-value conditions in plane angles and in bounded domains, dealing with the case where the support of nonlocal terms intersects the boundary. We establish necessary and…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
In this paper, we study a linear convection-diffusion equation with time-dependent coefficients on a bounded interval. The problem includes inhomogeneous Dirichlet boundary conditions and is motivated by physical models where the…
The focus of this paper is a non-local singular non-linear Fokker-Planck partial differential equation (PDE). The peculiarity of this PDE feature is in its divergence coefficient, which presents a product between a Besov distribution and a…
This work presents an alternative view on the numerical simulation of diffusion processes applied to the heat and moisture transfer through porous building materials. Traditionally, by using the finite-difference approach, the…
Using the theory of fixed point index, we discuss the existence and multiplicity of non-negative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a…
In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the…
Originating from the mathematical modelling of rainfall infiltration, we derive the solution of an initial-boundary value problem of a linear evolution partial differential equation, by using the Fokas method. We present numerical examples…
A broad class of inverse problems deals with determining certain parameters, from measurement data, in models which are associated to certain partial differential equations. In this work we focus on the heat equation on a finite interval…