On the dynamics of a class of nonclassical parabolic equations

DOI10.1016/J.JMAA.2005.06.094zbMath1092.35016OpenAlexW1988606518MaRDI QIDQ820042

Suyun Wang, De-Sheng Li, Cheng-Kui Zhong

Publication date: 6 April 2006

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2005.06.094

zbMATH Keywords

global attractorupper semicontinuitysoil mechanicsdecay estimatecontinuous dependencenon-Newtonian flownonclassical parabolic equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) PDEs in connection with fluid mechanics (35Q35)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the problem of diffusion in solids
• Infinite-dimensional dynamical systems in mechanics and physics.
• Long-time asymptotic behaviors of solutions of \(N\)-dimensional dissipative partial differential equations
• Well-posedness, blow up, and global existence for an integrable shallow water equation
• Viscous Cahn-Hilliard equation. II: Analysis
• Certain non-steady flows of second-order fluids
• On a theory of heat conduction involving two temperature
• Attractors of asymptotically compact processes and applications to nonlinear partial differential equations
• Necessary and sufficient conditions for the existence of global attractors for semigroups and applications
• An integrable shallow water equation with peaked solitons
• Dynamics of evolutionary equations

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