Nonlinear second order equations with applications to partial differential equations

DOI10.1016/0022-0396(85)90008-7zbMath0572.34004OpenAlexW2050902342MaRDI QIDQ1062196

Patricio Aviles, James T. jun Sandefur

Publication date: 1985

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

Full work available at URL: https://doi.org/10.1016/0022-0396(85)90008-7

zbMATH Keywords

energy estimatesCauchy problemcenter manifold theoremparabolic equationglobal existencehyperbolic equationsbifurcation of solutionssecond order semilinear differential equation

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12)

Related Items (26)

Energy convergence results for strongly damped nonlinear wave equations ⋮ Existence of regular solutions for semilinear parabolic integro- differential equations ⋮ Rothe's method to strongly damped wave equations ⋮ A problem with oblique derivative for some pseudoparabolic equations and equations close to them ⋮ Non-existence of global solutions to nonlinear wave equations with positive initial energy ⋮ Local and global existence of solutions to a strongly damped wave equation of the \(p\)-Laplacian type ⋮ A singular perturbation problem for nonlinear damped hyperbolic equations ⋮ Asymptotic behaviour of strongly damped nonlinear hyperbolic equations ⋮ Parabolic equations with nonlocal nonlinear source ⋮ Liapunov stability properties in second order evolution equations with finite memory ⋮ Global existence and blow-up for wave equation of \(p\)-Laplacian type ⋮ Qualitative behavior of solutions for a class of coupled nonlinear Klein-Gordon equations with strongly damping terms ⋮ Convergence of the strongly damped nonlinear Klein-Gordon equation in ℝⁿ with radial symmetry ⋮ Initial-boundary value problems for degenerate hyperbolic equations ⋮ On the Cauchy problem for a second order semilinear parabolic equation with factored linear part ⋮ Well-Posedness of Higher Order Abstract Cauchy Problems ⋮ Global existence and exponential stability of small solutions to nonlinear viscoelasticity ⋮ Local attractivity for integro-differential equations with noncompact semigroups ⋮ Convergence properties of the strongly damped nonlinear Klein-Gordon equation ⋮ Integrated semigroups and their application to complete second order Cauchy problems ⋮ A note on finite time blowup for dissipative Klein-Gordon equation ⋮ Finite-dimensional attractors for the quasi-linear strongly-damped wave equation ⋮ Global well-posedness of a class of fourth-order strongly damped nonlinear wave equations ⋮ On a global in time existence theorem of smooth solutions to a nonlinear wave equation with viscosity ⋮ Global existence, asymptotic behavior and blowup of solutions for a class of nonlinear wave equations with dissipative term ⋮ Energy decay rates and the dynamical von Karman equations

Cites Work

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• Boundary conditions and mode jumping in the buckling of a rectangular plate
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• Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis
• Decay and asymptotics for \(\square u = F(u)\)
• Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation
• Existence and Uniqueness of Solutions of Second Order Nonlinear Differential Equations
• A Bifurcation Problem for a Nonlinear Hyperbolic Partial Differential Equation
• On von kármán's equations and the buckling of a thin elastic plate, I the clamped plate

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