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arXiv · 2409.20321

Inverse coefficient problem for one-dimensional evolution equation vanishing initial condition

Oleg Y·Imanuvilov·Masahiro Yamamoto
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Abstract

We consider an inverse problem of determining a coefficient $p(x)$ of an evolution equation $\sigma\ppp_tu = a(x)\ppp_x^2u - p(x)u$ for $0 0$ and $T>0$ are arbitrarily given. Our main result is the uniqueness: by assuming that the zeros of initial value $b(x):= u(0,x)$ on $[0, \ell]$ is a finite set and each zero is of order one at most, if two solutions have the same Cauchy data at $x=0$ over $(0,T)$ and the same initial value $b(x)$, then the coefficient $p(x)$ is uniquely determined on $[0,\ell]$.

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Oleg Y, Imanuvilov, Masahiro Yamamoto. 2024-09-30. Inverse coefficient problem for one-dimensional evolution equation vanishing initial condition. https://arxiv.org/abs/2409.20321

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