Uniqueness, reconstruction and stability for an inverse problem of a semi-linear wave equation

Stability of an inverse problem for the discrete wave equation

Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation, discretized by finite differences in a 2-d uniform mesh, from boundary or internal measurements. The discrete stability results, when compared with their continuous counterpar...

On the seismic inverse problem: uniqueness, stability and reconstruction

Uniqueness and stability in an inverse problem for the Schrödinger equation

Local existence and uniqueness for a semi-linear accretive wave equation

We prove local existence and uniqueness of the solution (u, ut) ∈ C 0([0, T ];H1 × L2(RN )) of the semilinear wave equation utt −∆u = ut|ut| p−1 for 1 < p < 1 + 2 N .

Stability of an inverse problem for the discrete wave equation and convergence results

Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation, discretized by finite differences in a 2-d uniform mesh, from boundary or internal measurements. The discrete stability results, when compared with their continuous counterpar...