Non homogeneous Heat Equation: Identification and Regularization for the Inhomogeneous Term
Résumé
We study the nonhogeneous heat equation under the form: $ u_{t}-u_{xx}=\varphi (t)f(x)$, where the unknown is the pair of functions $ (u,f)$. Under various assumptions about the the function $ \varphi $ and the final value in $ t=1$ i.e. g(x), we propose different regularizations on this ill-posed problem based on the Fourier transform associated with a Lebesgue measure. For $ \varphi \not\equiv 0\ $the solution is unique.
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