Geodesic
Inverse coefficient problem for the semi-linear fractional telegraph equation
Electronic Journal of Differential Equations, Tome 2015 (2015).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We establish the unique solvability for an inverse problem for semi-linear fractional telegraph equation $$ D^\alpha_t u+r(t)D^\beta_t u-\Delta u=F_0(x,t,u,D^\beta_t u), \quad (x,t) \in \Omega_0\times (0,T] $$ with regularized fractional derivatives $$ \int_{\Omega_0}u(x,t)\varphi(x)dx=F(t), \quad t\in [0,T] $$ with given functions $\varphi$ and $F$.
Classification : 35S15
Keywords: fractional derivative, inverse boundary value problem, over-determination integral condition, Green's function, integral equation 
@article{EJDE_2015__2015__a35,
     author = {Lopushanska, Halyna and Rapita, Vitalia},
     title = {Inverse coefficient problem for the semi-linear fractional telegraph equation},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a35/}
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Lopushanska, Halyna; Rapita, Vitalia. Inverse coefficient problem for the semi-linear fractional telegraph equation. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a35/