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Identification of a diffusion coefficient in strongly degenerate parabolic equations with interior degeneracy | | Genni Fragnelli
; Gabriela Marinoschi
; Rosa Maria Mininni
; Silvia Romanelli
; | | Date: |
24 Jul 2013 | | Abstract: | We study two identification problems in relation with a strongly degenerate
parabolic diffusion equation characterized by a vanishing diffusion coefficient
$uin W^{1,infty},$ with the property $frac{1}{u}
otin L^{1}. $ The aim is
to identify $u$ from certain observations on the solution, by a technique of
nonlinear optimal control with control in coefficients. The existence of a
controller $u$ which is searched in $% W^{1,infty}$ and the determination of
the optimality conditions are given for homogeneous Dirichlet boundary
conditions. An approximating problem further introduced allows a better
characterization of the optimality conditions, due to the supplementary
regularity of the approximating state and dual functions and to a convergence
result. Finally, an identification problem with final time observation and
homogeneous Dirichlet-Neumann boundary conditions in the state system is
considered. By using more technical arguments we provide the explicit form of
$u$ and its uniqueness. | | Source: | arXiv, 1307.6393 | | Services: | Forum | Review | PDF | Favorites | |
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