Year: 2016
Type: preprint
Abstract: Let $u_t-a(t)u_{xx}=f(x, t)$ in $0\leq x \leq π,\,\,t\geq 0.$ Assume that $u(0,t)=u_1(t)$, $u(π,t)=u_2(t)$, $u(x,0)=h(x)$, and the extra data $u_x(0,t)=g(t)$ are known. The inverse problem is: {\it How does one determine the unknown $a(t)$?} The function $a(t)>a_0>0$ is assumed continuous and bounded. This question is answered and a method for recovery of $a(t)$ is proposed. There are several papers in which sufficient conditions are given for the uniqueness and existence of $a(t)$, but apparently there was no method proposed for calculating of $a$. The method given in this paper for proving the uniqueness and existence of the solution to inverse problem is new and it allows one to calculate the unknown coefficient $a(t)$.
Source: arXiv (Cornell University)
Author: Ramm, A. G.
Institution: Kansas State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4298093691