A Gronwall-type Lemma with parameter and dissipative estimates for PDEs

DOI10.1016/j.na.2008.03.015zbMath1167.34366OpenAlexW2031297906WikidataQ124791777 ScholiaQ124791777MaRDI QIDQ1004633

Vittorino Pata, Stefania Gatti, Serguei Zelik

Publication date: 11 March 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.03.015

zbMATH Keywords

Gronwall lemmadissipative estimate

Mathematics Subject Classification ID

Nonlinear differential equations in abstract spaces (34G20) Differential inequalities involving functions of a single real variable (34A40) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99)

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Cites Work

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• Weakly dissipative semilinear equations of viscoelasticity
• Attractors for semi-linear equations of viscoelasticity with very low dissipation
• Infinite-dimensional dynamical systems in mechanics and physics
• Global attractors for the wave equation with nonlinear damping
• Asymptotic stability in viscoelasticity
• Exponential stability in linear viscoelasticity
• Exponential attractors for a nonlinear reaction-diffusion system in
• Instability in Models Connected with Fluid Flows I
• SPATIALLY NONDECAYING SOLUTIONS OF THE 2D NAVIER-STOKES EQUATION IN A STRIP
• Attractors for semilinear strongly damped wave equations on \(\mathbb{R}^3\).