Related papers: The local backward heat problem
We consider Calder\'{o}n's inverse boundary value problems for a class of nonlinear Helmholtz Schr\"{o}dinger equations and Maxwell's equations in a bounded domain in $\R^n$. The main method is the higher-order linearization of the…
In this paper, a boundary integral method is used to solve an inverse linear heat conduction problem in two-dimensional bounded domain. An inverse problem of measuring the heat flux from partial (on part of the boundary) dynamic boundary…
In this paper, we study large-time asymptotics for heat and fractional heat equations in two discrete settings: the full lattice \(\mathbb Z^d\) and finite connected subgraphs with Dirichlet boundary condition. These results provide a…
In this article, we study an inverse boundary value problem for the time-dependent convection-diffusion equation. We use the nonlinear Carleman weight to recover the time-dependent convection term and time-dependent density coefficient…
We shall derive and propose several efficient overlapping domain decomposition methods for solving some typical linear inverse problems, including the identiffication of the flux, the source strength and the initial temperature in second…
This paper shows how the enclosure method which was originally introduced for elliptic equations can be applied to inverse initial boundary value problems for parabolic equations. For the purpose a prototype of inverse initial boundary…
We consider the formally determined inverse problem of recovering an unknown time-dependent potential function from the knowledge of the restriction of the solution of the wave equation to a small subset, subject to a single external…
In this paper, we consider a Cauchy problem for a first-order hyperbolic equation with time-dependent coefficients. Cauchy data are given on a lateral subboundary and we obtain local H\"older stabilities for inverse source and coefficient…
We study the boundary control problems for the wave, heat, and Schr\"odinger equations on a finite graph. We suppose that the graph is a tree (i.e., it does not contain cycles), and on each edge an equation is defined. The control is acting…
In this paper, we investigate the inverse problem on determining the spatial component of the source term in a hyperbolic equation with time-dependent principal part. Based on a newly established Carleman estimate for general hyperbolic…
We consider a heat conduction problem $S$ with mixed boundary conditions in a n-dimensional domain $\Omega$ with regular boundary $\Gamma$ and a family of problems $S_{\alpha}$, where the parameter $\alpha>0$ is the heat transfer…
We develop a backward-in-time machine learning algorithm that uses a sequence of neural networks to solve optimal switching problems in energy production, where electricity and fossil fuel prices are subject to stochastic jumps. We then…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
We prove integrated local energy decay for solutions of the damped wave equation with time-dependent damping satisfying an appropriate generalization of the geometric control condition on asymptotically flat, stationary space-times. We…
This paper is devoted to the study of the one dimensional non homogeneous heat equation coupled to Dirichlet Boundary Conditions. We obtain the explicit expression of the solution of the linear equation by means of a direct integral in an…
We find integrability conditions on the initial data $f$ for the existence of solutions of the Heat problem on the Heisenberg group. From this result we characterize the weighted Lebesgue spaces for which the solutions exists a.e. when the…
This paper presents a combined field and boundary integral equation method for solving the time-dependent scattering problem of a thermoelastic body immersed in a compressible, inviscid and homogeneous fluid. The approach here is a…
We present a Waveform Relaxation (WR) version of the Dirichlet-Neumann algorithm, formulated specially for multiple subdomains splitting for general parabolic and hyperbolic problems. This method is based on a non-overlapping spatial domain…
In meteorological and oceanological studies the classical approach for finding the numerical solution of the regional model consists in formulating and solving the Cauchy-Dirichlet problem. The related boundary conditions are obtained by…