On nonlinear wave equations with degenerate damping and source terms

DOI10.1090/S0002-9947-05-03880-8zbMath1065.35193MaRDI QIDQ4663477

Viorel Barbu, Mohammad A. Rammaha, Irena Lasiecka

Publication date: 31 March 2005

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

energy estimatessub-differentialblow up of solutionsGalerkin approximation schemeKakutani's theorem.

Mathematics Subject Classification ID

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compact sets in the space \(L^ p(0,T;B)\)
• Non homogeneous boundary value problems for second order hyperbolic operators
• Das Anfangswertproblem im Großen für eine Klasse nichtlinearer Wellengleichungen
• Nonlinear evolution equations - global behavior of solutions
• Saddle points and instability of nonlinear hyperbolic equations
• Global nonexistence for abstract evolution equations with positive initial energy
• Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave equation
• Existence of a solution of the wave equation with nonlinear damping and source terms
• Global nonexistence theorems for quasilinear evolution equations with dissipation
• Global existence and nonexistence theorems for quasilinear evolution equations of formally parabolic type
• Existence for a nonlinear wave equation with damping and source terms.
• Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms
• Global solutions to boundary value problems for a nonlinear wave equation in high space dimensions.
• Caractérisation de quelques espaces d'interpolation
• Non-linear semi-groups
• Blow-up theorems for nonlinear wave equations
• Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation
• REMARKS ON BLOW-UP AND NONEXISTENCE THEOREMS FOR NONLINEAR EVOLUTION EQUATIONS
• Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms
• Global existence and non-existence theorems for nonlinear wave equations
• Global existence and nonexistence for nonlinear wave equations with damping and source terms
• Global solvability and uniform decays of solutions to quaslinear equation with nonlinear boundary dissipation
• Mixed problem for some semi-linear wave equation with a nonhomogeneous condition
• Instability and Nonexistence of Global Solutions to Nonlinear Wave Equations of the Form Pu tt = -Au + ℱ(u)
• Some non-linear evolution equations
• Équations différentielles abstraites
• Interpolation in $L^{p}$ with boundary conditions

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