Scattering problems for symmetric systems with dissipative boundary conditions
Idioma
en
Chapitre d'ouvrage
Este ítem está publicado en
Studies in Phase Space Analysis with Applications to PDEs, Studies in Phase Space Analysis with Applications to PDEs. 2013p. 337-353
Birkhäuser
Resumen en inglés
We study symmetric systems with dissipative boundary conditions. The solutions of the mixed problems for such systems are given by a contraction semigroup $V(t)f = e^{tG_b}f, t \geq 0$. The solutions $u(t, x) = V(t)f$, ...Leer más >
We study symmetric systems with dissipative boundary conditions. The solutions of the mixed problems for such systems are given by a contraction semigroup $V(t)f = e^{tG_b}f, t \geq 0$. The solutions $u(t, x) = V(t)f$, where $f$ is an eigenfunction of the generator $G_b$ with eigenvalue $\lambda,\Re \lambda < 0,$ are called asymptotically disappearing (ADS). We prove that the wave operators are not complete if there exist (ADS). This is the case for Maxwell system with special boundary conditions in the exterior of the sphere. We obtain a representation of the scattering kernel and we examine the inverse back-scattering problem related to the leading term of the scattering kernel.< Leer menos
Palabras clave en inglés
dissipative boundary conditions
asymptotically disappearing solutions
inverse scattering problems
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