Related papers: Initial-boundary value problems for multi-term tim…
Inverse problem to determine simultaneously a general space- and time-dependent source and an initial state in a fractional diffusion equation from an {\it a posteriori} measurement of the normal derivative of the state on a portion of a…
We consider the terminal value problem (or called final value problem, initial inverse problem, backward in time problem) of determining the initial value, in a general class of time-fractional wave equations with Caputo derivative, from a…
We study a local data inverse problem for the time-dependent Convection-Diffusion Equation (CDE) in a bounded domain where a part of the boundary is treated to be inaccessible. Up on assuming the inaccessible part to be flat, we seek for…
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…
This paper is concerned with initial-boundary-value problems (IBVPs) for a class of nonlinear Schr\"odinger equations posed either on a half line $\mathbb{R}^+$ or on a bounded interval $(0, L)$ with nonhomogeneous boundary conditions. For…
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…
In the paper, the initial-boundary value problems to a semilinear integro-differential equation with multi-term fractional Caputo derivatives are analyzed. A particular case of this equation models oxygen diffusion through capillaries.…
In this paper, we consider the direct and inverse problem for time-fractional diffusion in a domain with an impenetrable subregion. Here we assume that on the boundary of the subregion the solution satisfies a generalized impedance boundary…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
This paper discusses the initial-boundary-value problems (IBVP) of nonlinear Schr\"odinger equations posed in a half plane $\mathbb{R} \times \mathbb{R}^+$ with nonhomogeneous Dirichlet boundary conditions. For any given $s \ge 0$, if the…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
We study the Schwartz class of initial-boundary value (IBV) problems for the integrable Fokas-Lenells equation on the half-line via the Deift-Zhou's nonlinear descent method analysis of the corresponding Riemann-Hilbert problem such that…
We study an initial value problem for the one-dimensional non-stationary linear Schr\"odinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems…
In this paper, we consider forward and inverse problems for subdiffusion equations with time-dependent coefficients. The fractional derivative is taken in the sense of Riemann-Liouville. Using the classical Fourier method, the theorem of…
Difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$ and $\beta$ are considered. By the method of energy inequalities, for the solution…
In this paper, we present an inverse problem of identifying the reaction coefficient for time fractional diffusion equations in two dimensional spaces by using boundary Neumann data. It is proved that the forward operator is continuous with…
In this paper, we are interested in the study of a problem with fractional derivatives having boundary conditions of integral types. The problem represents a Caputo type advection-diffusion equation where the fractional order derivative…
This article is devoted to the simultaneous resolution of three inverse problems, among the most important formulation of inverse problems for partial differential equations, stated for some class of diffusion equations from a single…
We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit…
We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…