Energy decay for differential inequalities in a Hilbert space with applications to ultrahyperbolic equations

DOI10.1016/0022-0396(80)90015-7zbMath0466.35011OpenAlexW2001674680MaRDI QIDQ1155185

Hajimu Ogawa

Publication date: 1980

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(80)90015-7

zbMATH Keywords

ordinary differential operatorLipschitz conditionenergy decayultrahyperbolic operatorHilbert space A. C. Murraysecond-order linear elliptic operatorsweighted quadratic functional

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Partial differential inequalities and systems of partial differential inequalities (35R45) First-order nonlinear hyperbolic equations (35L60) Hyperbolic equations and hyperbolic systems (35L99) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20)

Cites Work

• Asymptotic behavior and uniqueness for an ultrahyperbolic equation with variable coefficients
• Energy decay for solutions of ultrahyperbolic inequalities
• Some uniqueness and growth theorems in the Cauchy problem for \(Pu_{tt}+Mu_t+Nu=0\) in Hilbert space
• Asymptotic Behavior and Lower Bounds for Semilinear Wave Equations in Hilbert Space with Applications
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