19-40 Vitali Vougalter
Inverse problems for some systems of parabolic equations with coefficient depending on time (82K, pdf) Jun 18, 19
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Abstract. We consider the system u_{t}-a(t)Mu_{xx}=f(x,t), where 0\leq x\leq \pi, t\geq 0, assuming that u(0,t)=u_{1}(t), u(\pi, t)=u_{2}(t), u(x, 0)=h(x), and the extra data u_{x}(0,t)=g(t) are known. The coupling matrix M is a real, diagonalizable matrix for which all of the eigenvalues are positive reals. The inverse problem is: How does one determine the unknown a(t)? The function a(t) is assumed positive, continuous and bounded. This problem is solved and a method to recover a(t) is proposed. The method presented in this work enables us to evaluate the unknown coefficient a(t) in closed form if the data (which can be chosen by experimenter) are properly chosen.

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