Energy bounds for some nonstandard problems in partial differential equations.

DOI10.1016/S0022-247X(02)00208-1zbMath1121.35331OpenAlexW2052592987MaRDI QIDQ1856819

Philip W. Schaefer, Lawrence E. Payne

Publication date: 11 February 2003

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0022-247x(02)00208-1

Mathematics Subject Classification ID

Linear differential equations in abstract spaces (34G10) Abstract hyperbolic equations (35L90)

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Cites Work

• Unnamed Item
• Unnamed Item
• The Dirichlet problem for the wave equation
• Uniqueness and growth of weak solutions to certain linear differential equations in Hilbert space
• Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings
• The condition for uniqueness of solutions of the Dirichlet problem for the wave equation in coordinate rectangles
• Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics
• Some uniqueness and growth theorems in the Cauchy problem for \(Pu_{tt}+Mu_t+Nu=0\) in Hilbert space
• Lower Bounds and Uniqueness Theorems for Solutions of Differential Equations in a Hilbert Space
• Infinite Systems of Nonlinear Oscillation Equations Related to the String
• Infinite Systems of Nonlinear Oscillation Equations with Linear Damping
• The Dirichlet problem for the vibrating string equation
• Decay rate of solutions of a wave equation with damping and external force