Initial-boundary value problem for second order hyperbolic operator with mixed boundary conditions

2024/01/09 by Djamel Ait-Akli, Ait-Akli, Djamel
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Stability and Controllability of Differential Equations #Differential Equations and Boundary Problems

paper · pdf · doi:10.48550/arxiv.2401.04396

Abstract

We deal with a linear hyperbolic differential operator of the second order on a bounded planar domain with a smooth boundary. We establish a well-posedness result in case where a mixed, Dirichlet-Neumann, condition is prescribed on the boundary. We focus on the case of a non-homogeneous Dirichlet data and a homogeneous Neumann one. The presented proof is based on a functional theoretical approach and on an approximation argument. Moreover, this work discuss an improvement of a result concerning the range of some operators related to the considered hyperbolic PDE yielding characterizations for the range space of these operators.

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