A gradient-based approach for identification of the zeroth-order coefficient 𝑝(𝑥) in the parabolic equation 𝑢𝑡 = (𝑘(𝑥)𝑢𝑥)𝑥 − 𝑝(𝑥)𝑢 from Dirichlet-type measured output
Makaleler > Tam Makale · 2018
Yazarlar: Pınar Barış Şahin
Journal of Inverse and Ill-posed Problems, Uluslararası, Wos, 2018, cilt 27, ss 185-193
Özet
Abstract This paper is devoted to the inverse problem of identifying an unknown spacewise-dependent zeroth-order coefficient p ( x ) {p(x)} in the 1D diffusion equation u t = ( k ( x ) u x ) x - p ( x ) u {u_{t}=(k(x)u_{x})_{x}-p(x)u} from boundary Dirichlet measured output f ( t ) :- u ( 0 , t ) {f(t)\coloneq u(0,t)} , t ∈ [ 0 , T ] {t\in[0,T]} . Compactness and Lipschitz continuity of the input-output operator Φ [ p ] :- u ( x , t ; p ) | x = 0 + {\Phi[p]\coloneq u(x,t;p)|_{x=0^{+}}} , Φ [ ⋅ ] : 𝒫 ⊂ H 1