Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay

DOI10.1007/s00526-007-0096-7zbMath1131.35036OpenAlexW2058581427MaRDI QIDQ2642939

Hans-Christoph Grunau, Gazzola, Filippo

Publication date: 6 September 2007

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00526-007-0096-7

zbMATH Keywords

decay rateinstability of the zero steady statestability of the zero steady state

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Stability in context of PDEs (35B35) Critical exponents in context of PDEs (35B33) Initial value problems for higher-order parabolic equations (35K30) Higher-order parabolic equations (35K25)

Related Items

Existence of solutions to nonlinear parabolic equations via majorant integral kernel, Existence of solutions to fractional semilinear parabolic equations in Besov-Morrey spaces, Effect of decay rates of initial data on the sign of solutions to Cauchy problems of polyharmonic heat equations, Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations, Wide oscillation finite time blow up for solutions to nonlinear fourth-order differential equations, Global solutions for a nonlinear integral equation with a generalized heat kernel, Existence of solutions for a higher-order semilinear parabolic equation with singular initial data, Critical and supercritical higher order parabolic problems in \(\mathbb R^N\), Refined asymptotics for entire solutions of a biharmonic equation with a supercritical nonlinearity, Existence of positive solutions of a semilinear elliptic equation with a dynamical boundary condition, Some new properties of biharmonic heat kernels, Large time behavior of ODE type solutions to higher-order semilinear parabolic equations with small initial data, Asymptotics for a nonlinear integral equation with a generalized heat kernel, Solvability of superlinear fractional parabolic equations, Nonexistence of global solutions for quasilinear backward parabolic inequalities with \(p\)-Laplace-type operator

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