Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 13 August 2020Accepted: 08 December 2020Published online: January 2021Keywordsfractional partial differential equations, inverse problems, Runge approximation propertyAMS Subject Headings35R11, 35R30Publication DataISSN (print): 0036-1410ISSN (online): 1095-7154Publisher:...

This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. ...

We investigate uniqueness in the inverse problem of reconstructing simultaneously a spacewise conductivity function and a heat source in the parabolic heat equation from the usual conditions of the direct problem and additional information from a supplementary temperature measurement at a given single instant of time. In the multi-dimensional case, we use Carleman estimates for parabolic equati...

The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary value inputs.

We consider a semilinear parabolic equation in a rectangular domain Ω ⊂ R: (∂tu)(x, t) = ∆u(x, t) + a(u(x, t)) with the zero initial value and suitable Dirichlet data. We discuss an inverse problem of determining the nonlinear term a(·) from Neumann data ∂u ∂n on ∂Ω × (0, T ). Under appropriate Dirichlet data, we prove conditional stability of the Hölder type in this inverse problem within a su...

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A problem of dynamical reconstruction of unknown distributed or boundary disturbances acting upon nonlinear parabolic equations is discussed. A regularized algorithm which allows us to reconstruct disturbances synchro with the process under consideration is designed. This algorithm is stable with respect to informational noises and computational errors.

We study asymptotic proximity as t ! 1 of the solutions of the inverse problem for a pseudo-parabolic equation with an unknown source function. The overdetermination condition is given in integral form. 2003 Elsevier Inc. All rights reserved.

The practical aspect in the parareal algorithm that it consist of using two solvers over different time stepping, the coarse and fine solvers to produce a rapid convergent iterative method for multi processors computations. The coarse solver solve the equation sequentially on the coarse time step while the fine solver use the information from the coarse solution to solve, in parallel, over the ...