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Asymptotic behaviour of the solutions of inverse problems for pseudo-parabolic equations. (English) Zbl 1059.35181

Summary: We study asymptotic proximity as \(t\to \infty\) of the solutions of the inverse problem for the pseudo-parabolic equation \[ u_t(x,t)- \Delta u_t(x,t)- \Delta u(x,t)+ \alpha u(x,t)= f(t) g(x,t), \quad Q_\infty= \Omega\times (0,\infty) \] with an unknown source function \(f\). The overdetermination condition is given in integral form.

MSC:

35R30 Inverse problems for PDEs
35K70 Ultraparabolic equations, pseudoparabolic equations, etc.
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References:

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