GLOBAL SOLUTIONS AND DECAY PROPERTY WITH REGULARITY-LOSS FOR QUASI-LINEAR HYPERBOLIC SYSTEMS WITH DISSIPATION

DOI10.1142/S0219891613500021zbMath1275.35140OpenAlexW1975156027MaRDI QIDQ2836509

Priyanjana M. N. Dharmawardane

Publication date: 3 July 2013

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

Full work available at URL: https://doi.org/10.1142/s0219891613500021

zbMATH Keywords

small initial datanonlocal termmemorypolynomial decaytime-weighted energy method

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear constitutive equations for materials with memory (74D10) Second-order quasilinear hyperbolic equations (35L72) Initial value problems for second-order hyperbolic systems (35L52)

Related Items (5)

A dissipative logarithmic-Laplacian type of plate equation: asymptotic profile and decay rates ⋮ The frequency-localization technique and minimal decay-regularity for Euler-Maxwell equations ⋮ Some hyperbolic conservation laws on \(\mathbb{R}^n\) ⋮ \(L^p - L^q - L^r\) estimates and minimal decay regularity for compressible Euler-Maxwell equations ⋮ Asymptotic profiles for damped plate equations with rotational inertia terms

Cites Work

• Global solutions to quasi-linear hyperbolic systems of viscoelasticity
• Decay property for a plate equation with memory-type dissipation
• Decay property for second order hyperbolic systems of viscoelastic materials
• Global existence and exponential stability of small solutions to nonlinear viscoelasticity
• Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory
• Decay Estimates of Solutions for Quasi-Linear Hyperbolic Systems of Viscoelasticity
• GLOBAL EXISTENCE AND DECAY OF SOLUTIONS FOR A QUASI-LINEAR DISSIPATIVE PLATE EQUATION
• DECAY PROPERTY FOR THE TIMOSHENKO SYSTEM WITH MEMORY-TYPE DISSIPATION
• DECAY PROPERTY OF REGULARITY-LOSS TYPE AND APPLICATION TO SOME NONLINEAR HYPERBOLIC–ELLIPTIC SYSTEM
• DECAY PROPERTY OF REGULARITY-LOSS TYPE FOR DISSIPATIVE TIMOSHENKO SYSTEM
• DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR DISSIPATIVE TIMOSHENKO SYSTEM
• Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems with a convex entropy

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