An 'optimal filtering' method for the sideways heat equation
- 1 August 1990
- journal article
- research article
- Published by IOP Publishing in Inverse Problems
- Vol. 6 (4) , 681-696
- https://doi.org/10.1088/0266-5611/6/4/013
Abstract
The authors consider a Cauchy problem for the heat equation in the quarter plane, where data are given at x=x and they want to determine a solution for 0<x<x. This problem, which can be called the sideways heat equation, is ill-posed: the solution (if it exists) does not depend continuously on the data. Continuous dependence is restored if a bound is imposed on the solution at x=0, and Holder-type error estimates can be obtained for this stabilised problem. They consider a filtering method (defined using the Fourier transform) for computing an approximate solution of the sideways heat equation.Keywords
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