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On the uniqueness of solution Cauchy’s inverse problem for the equation $$\Delta u=au+b$$. (English) Zbl 1229.35321
Summary: The inverse Cauchy problem
$\Delta u(x)=au(x)+b\geq 0 \quad\text{for }x\in \omega \text{ and }u=0, \qquad \frac{\partial u}{\partial\nu}=\Phi \quad\text{on }\gamma$
is shown as having a unique solution within a wide class of simply connected domains $$\omega\Subset\mathbb R^2$$ with smooth boundary $$\gamma$$. Here $$a$$ and $$b$$ are real numbers to be determined, and $$\Phi$$ is a given function which is normalized by the condition $$\int_\gamma \Phi\,ds=1$$.

##### MSC:
 35R30 Inverse problems for PDEs 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness 76W05 Magnetohydrodynamics and electrohydrodynamics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 35Q82 PDEs in connection with statistical mechanics 82D75 Nuclear reactor theory; neutron transport
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