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Fourier regularization method for solving the surface heat flux from interior observations. (English) Zbl 1122.80016

From the text: In the present paper, a Fourier regularization method for solving the surface heat flux distribution from interior observations with some estimates is given. A numerical example is also provided.
The forward problem is the heat equation in the quarter plane: \[ \begin{cases} u_ t = u_ {xx}, \quad &t>0,\;x>0,\\ u(0, t) = f(t), \quad &t > 0,\\ u(x, 0) = 0, \quad &x > 0, \end{cases} \] where the boundary condition \(f\) is assumed to be in the Sobolev space \(H^ p(\mathbb{R})\) for some \(p \geq 0\). The inverse problem is to find \(u(x,t)\) and its gradient with respect to \(x\), \(u_x(x,t)\), for \(0\leq x<1\).

MSC:

80M25 Other numerical methods (thermodynamics) (MSC2010)
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35R25 Ill-posed problems for PDEs
80A23 Inverse problems in thermodynamics and heat transfer
35R30 Inverse problems for PDEs
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References:

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