LOCAL WELL POSEDNESS OF CAUCHY PROBLEM FOR VISCOUS DIFFUSION EQUATIONS

DOI10.1142/S0129167X09005364zbMath1183.35156OpenAlexW2045847667MaRDI QIDQ3632275

Run-Zhang Xu, Ya-Cheng Liu

Publication date: 23 June 2009

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129167x09005364

zbMATH Keywords

\(W^{k,p}\) solutionequivalent integral equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Degenerate parabolic equations (35K65) Initial value problems for second-order parabolic equations (35K15) Blow-up in context of PDEs (35B44)

Cites Work

• Global existence and asymptotics of solutions of the Cahn-Hilliard equation
• The Cauchy problem for the generalized IMBq equation in \(W^{s,p}(\mathbb R^n)\).
• Uniqueness of solutions to a viscous diffusion equation.
• Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term
• Some Additional Remarks on the Nonexistence of Global Solutions to Nonlinear Wave Equations
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