On a nonlinear evolution equation and its applications

DOI10.1016/0362-546X(94)00193-LzbMath0828.34050OpenAlexW1987704935MaRDI QIDQ4839248

A. C. Biazutti

Publication date: 17 July 1995

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

Full work available at URL: https://doi.org/10.1016/0362-546x(94)00193-l

zbMATH Keywords

existenceasymptotic behavioruniquenessabstract Cauchy problemnonlinear operatorsnonlinear hyperbolic problems

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Asymptotic properties of solutions to ordinary differential equations (34D05) Initial value problems for higher-order hyperbolic equations (35L30)

Related Items (25)

Local and global existence of solutions to a strongly damped wave equation of the \(p\)-Laplacian type ⋮ Decay rate estimates for a class of quasilinear hyperbolic equations with damping terms involving p-Laplacian ⋮ Global existence, uniqueness, and asymptotic behavior of solution for \(p\)-Laplacian type wave equation ⋮ Weak solutions and blow-up for wave equations of p-Laplacian type with supercritical sources ⋮ Exponential stability for a plate equation with p-Laplacian and memory terms ⋮ Asymptotic behaviour of solutions for \(p\)-Laplacian wave equation with \(m\)-Laplacian dissipation ⋮ On wave equations of the \(p\)-Laplacian type with supercritical nonlinearities ⋮ Global existence and blow-up for wave equation of \(p\)-Laplacian type ⋮ Global existence, energy decay, and blowup of solutions for a wave equation type \(p\)-Laplacian with memory term and dynamic boundary conditions ⋮ On weak solutions for hyperbolic differential inclusion with discontinuous nonlinearities ⋮ Periodic homogenization of parabolic nonstandard monotone operators ⋮ Existence and blow up for a nonlinear hyperbolic equation with anisotropy ⋮ CONVERGENCE OF QUASI-LINEAR HYPERBOLIC EQUATIONS ⋮ Mechanical models of artery walls ⋮ Relaxation of regularity for the Westervelt equation by nonlinear damping with applications in acoustic-acoustic and elastic-acoustic coupling ⋮ Global well-posedness for a class of fourth-order nonlinear strongly damped wave equations ⋮ Abstract wave equation with monotone operator damping in Banach spaces ⋮ Cauchy problem for quasi-linear wave equations with nonlinear damping and source terms ⋮ Global and blow-up solutions for a system of nonlinear hyperbolic equations with dissipative terms ⋮ Cauchy problem for quasi-linear wave equations with viscous damping ⋮ Viscous solutions on some nonlinear wave equations ⋮ On a nonlinear hyperbolic equation with anisotropy: Global existence and decay of solution ⋮ Blow-up phenomenon for a nonlinear wave equation with anisotropy and a source term ⋮ Attractors for the strongly damped wave equation with p‐Laplacian ⋮ Long-time asymptotic expansion for the damped semilinear wave equation.

Cites Work

• Note on certain nonlinear evolution equations of second order
• Decay of solutions of some nonlinear evolution equations
• A difference inequality and its application to nonlinear evolution equations
• Nonlinear functional equations in Banach spaces and elliptic super- regularization
• Strong Solutions of a Quasilinear Wave Equation with Nonlinear Damping
• On the decay of solutions for some nonlinear evolution equations of second order
• Some nonlinear evolution equations of second order
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