19-32 C. Connell McCluskey, Vitali Vougalter

Inverse problems for some systems of parabolic equations (86K, pdf) Apr 25, 19

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Abstract. We study the system u_{t}-Au_{xx}=h(t), where 0\leq x\leq \pi, t\geq 0, assuming that u(0, t)=v(t), u(\pi, t)=0, and u(x, 0)=g(x). The coupling matrix A is a real, diagonalizable matrix for which all of the eigenvalues are positive reals. The question is: What extra data determine the three unknown vector functions {h, v, g} uniquely? This problem is solved and an analytical method for the recovery of the above three vector functions is presented.

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