An approach for recovering initial temperature via a bounded linear time sampling

Recovery of an initial temperature of a one-dimensional body from finite time-observations

“…This type of inverse problem is highly ill-posed unless further assumptions on f , x 0 and t k are made. It has been widely studied in recent times (see [1,2,6,8,9,10,11]) and has applications in many areas (see [3,7,12,13]). Under the Dirichlet boundary conditions (i. e., u(0, t) = u(0, π) = 0), DeVore and Zuazua ( [6]) have studied an analogous problem by assuming that f is in…”

“…, n for a large n, they constructed an approximation to f in L 2 ([0, π]) with an accuracy of order n −r . Aryal and Karki ( [2]) have selected n forward times t k , k = 1, 2, 3, . .…”

“…In this paper, we will use the approach of Aryal and Karki ( [2]) and establish a result corresponding to the initial-boundary value problem described in (1.1). For this, we consider a finite time interval [0, T ] and select n forward times t 1 and t k , k = 2, 3, .…”

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Under the Dirichlet boundary setting, Aryal and Karki (2022) studied an inverse problem of recovering an initial temperature profile from known temperature measurements at a fixed location of a one-dimensional body and at linearly growing finitely many later times within a bounded interval. This paper studies the problem under the Neumann boundary conditions.

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