On bounds for solutions to nonlinear wave equations in Hilbert space with applications to nonlinear elastodynamics

DOI10.1007/BF01595135zbMath0335.35065OpenAlexW2061585712MaRDI QIDQ1229365

Frederick Bloom

Publication date: 1976

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01595135

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) First-order nonlinear hyperbolic equations (35L60) A priori estimates in context of PDEs (35B45)

Cites Work

• Unnamed Item
• Non-existence, instability, and growth theorems for solutions of a class of abstract nonlinear equations with applications to nonlinear elasto- dynamics
• Uniqueness and growth of weak solutions to certain linear differential equations in Hilbert space
• Continuous dependence on initial geometry for a class of abstract equations in Hilbert space
• Some stability theorems for an abstract equation in Hilbert space with applications to linear elastodynamics
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time
• Logarithmic convexity and the Cauchy problem for some abstract second order differential inequalities
• Growth estimates for solutions of evolutionary equations in Hilbert space with applications in elastodynamics
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Logarithmic Convexity, First Order Differential Inequalities and Some Applications
• On the Uniquenes of Bounded Solutions to $u'(t) = A(t)u(t)$ and $u(t) = A(t)u(t)$ in Hilbert Space

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