Global existence of classical solutions to the initial-boundary value problem of the semilinear wave equations with a degenerate dissipative term

DOI10.1016/0362-546X(90)90117-YzbMath0732.35045OpenAlexW2001582299MaRDI QIDQ3357566

Mitsuhiro Nakao

Publication date: 1990

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(90)90117-y

zbMATH Keywords

initial boundary value problemselfadjoint uniformly elliptic operator

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70)

Related Items

Strong decay for wave equations with nonlinear nonmonotone damping ⋮ On periodic solutions of a semilinear hyperbolic parabolic equation ⋮ Global nonexistence of solutions for viscoelastic wave equations of Kirchhoff type with high energy ⋮ Existence of global classical solutions of the initial-boundary value problem for some nonlinear wave equations ⋮ Decay of solutions of the wave equation with some localized dissipations ⋮ Existence of global smooth solutions to the initial-boundary value problem for the quasi-linear wave equation with a degenerate dissipative term ⋮ Decay of solutions of the wave equation with a local degenerate dissipation

Cites Work

• Unnamed Item
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• Existence of global classical solutions of the initial-boundary value problem for some nonlinear wave equations
• Semigroups of linear operators and applications to partial differential equations
• Global existence of small solutions to nonlinear evolution equations
• Regular solutions of initial-boundary value problems for linear and nonlinear wave-equations. II
• On the existence of global classical solution of initial-boundary value problem for \(\square u-u^3=f\)
• Global existence and asymptotics of the solutions of the second-order quasilinear hyperbolic equations with the first-order dissipation
• A difference inequality and its application to nonlinear evolution equations
• Sur \(\square u+u^3=f\) dans un domaine noncylindrique
• Die Existenz regulärer Lösungen für Cauchy- und Anfangs- Randwertprobleme nichtlinearer Wellengleichungen
• The existence of a global classical solution of the initial boundary value problem for \(\square u+u^ 3 = f\)
• Klassische Lösungen nichtlinearer Wellengleichungen im Großen
• Ein Anfangswertproblem für hyperbolische Gleichungen mit nichtlinearem elliptischen Hauptteil
• Periodic solutions of nonlinear wave-equations with a dissipative term
• Energy decay for the wave equation with a degenerate dissipative term
• CONVERGENCE OF SOLUTIONS OF THE WAVE EQUATION WITH A NONLINEAR DISSIPATIVE TERM TO THE STEADY STATE