On the Neumann problem of linear hyperbolic parabolic coupled systems

Abstract

We prove the unique existence of solutions to some mixed problem of hyperbolic parabolic coupled systems with Neumann boundary condition, and we investigate how the constant in the first energy estimate depends on the coefficients of the opertors.

On finding a cavity in a thermoelastic body using a single displacement measurement over a finite time interval on the surface of the body

“…It is based on the Hille-Yoshida theorem. By applying Theorem 2.1 in [4] to the present case, we see that the initial boundary value problem (1.1) has a unique solution such that 3 ) and G(0) = 0. We say that the pair (f, G) is admissible if the conditions listed above are satisfied.…”

“…It is based on the Hille-Yoshida theorem. By applying Theorem 2.1 in [4] to the present case, we see that the initial boundary value problem (1.1) has a unique solution such that…”

“…It is assumed that Ω \ D is homogeneous and isotropic. In this paper, for simplicity and considering the results in [4], we assume that Ω is given by a bounded domain with C ∞ -boundary and D a nonempty bounded open subset of Ω with C ∞ -boundary such that Ω \ D is connected. We use the same symbol ν to denote both the outer unit normal vectors of ∂D and ∂Ω.…”

“…Before describing the problem, we specify the class where the solution of (1.1) lives. We employ a general result on the unique solvability and regularity of the initial boundary value problem for the coupled system of the parabolic and hyperbolic system with inhomogeneous Neumann-type boundary condition established in [4]. It is based on the Hille-Yoshida theorem.…”

The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell-type initial data

“…The direct problem has been studied in [2] in a more general setting under the assumption that both ∂Ω and ∂D are smooth. In this section we employ this smoothness assumption.…”