zbMATH — the first resource for mathematics

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 \(\int_\gamma \Phi\,ds=1\).

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
Full Text: Link