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Asymptotics for 2‐D wave equations with Wentzell boundary conditions in the square
Author(s) -
Li Chan,
Jin KunPeng
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6729
Subject(s) - mathematics , eigenvalues and eigenvectors , mathematical analysis , operator (biology) , square (algebra) , boundary (topology) , boundary value problem , spectrum (functional analysis) , matrix (chemical analysis) , wave equation , cauchy distribution , geometry , physics , quantum mechanics , biochemistry , chemistry , materials science , repressor , transcription factor , composite material , gene
This paper concerns the asymptotics of the linear wave equation with frictional damping only on Wentzell boundary in the square. After reformulating the model into an abstract Cauchy problem, we show that the spectrum for the corresponding operator matrix has no purely imaginary values. Moreover, by analyzing a family of eigenvalues for the operator matrix, we prove that there exists a solution of the system, whose energy decay rate can be arbitrarily slow.