Blowup for a Fourth-Order Parabolic Equation with Gradient Nonlinearity

DOI10.1137/19M1253654zbMath1431.35057OpenAlexW3007000234MaRDI QIDQ5218229

Kazuhiro Ishige, Shinya Okabe, Nobuhito Miyake

Publication date: 2 March 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/19m1253654

zbMATH Keywords

fourth-order parabolic equationblowupepitaxial growthgradient nonlinearity

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Thin films (74K35) Existence of solutions of dynamical problems in solid mechanics (74H20) PDEs in connection with mechanics of deformable solids (35Q74) Higher-order parabolic equations (35K25) Blow-up in context of PDEs (35B44)

Related Items

Existence of solutions to nonlinear parabolic equations via majorant integral kernel ⋮ Global existence and blow-up of weak solutions for a fourth-order parabolic equation with gradient nonlinearity ⋮ Well-posedness and stability for a class of fourth-order nonlinear parabolic equations ⋮ Well-posedness and dynamic properties of solutions to a class of fourth order parabolic equation with mean curvature nonlinearity ⋮ Existence of solutions for a higher-order semilinear parabolic equation with singular initial data ⋮ Asymptotic Behavior of Solutions for a Fourth Order Parabolic Equation with Gradient Nonlinearity via the Galerkin Method ⋮ Existence and limit problem for fractional fourth order subdiffusion equation and Cahn-Hilliard equation ⋮ Suppression of epitaxial thin film growth by mixing

Cites Work

• Unnamed Item
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• Heat equation with a nonlinear boundary condition and uniformly local \(L^r\) spaces
• Decay and local eventual positivity for biharmonic parabolic equations
• Saddle points and instability of nonlinear hyperbolic equations
• A fourth-order parabolic equation modeling epitaxial thin film growth
• Local and global existence of solutions to semilinear parabolic initial value problems
• Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian
• Some nonexistence and instability theorems for solutions of formally parabolic equations of the form \(Pu_t=-Au+ {\mathfrak F} (u)\)
• Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition
• A continuum model of kinetic roughening and coarsening in thin films
• Heat equation with a nonlinear boundary condition and growing initial data.
• Global solutions for a nonlinear integral equation with a generalized heat kernel
• Supersolutions for a class of nonlinear parabolic systems
• Existence and blow-up for higher-order semilinear parabolic equations: Majorizing order-preserving operators
• Classical Fourier Analysis