Asymptotic behavior for a fourth-order parabolic equation involving the Hessian

DOI10.1007/s00033-018-1034-6zbMath1406.35145OpenAlexW2899525069WikidataQ128972539 ScholiaQ128972539MaRDI QIDQ1757314

Jun Zhou, Guangyu Xu

Publication date: 3 January 2019

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-018-1034-6

zbMATH Keywords

fourth-order parabolic equationglobal existenceblowupepitaxial growthenergy decayexponential growth (decay)Hessian term

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Higher-order parabolic equations (35K25) Blow-up in context of PDEs (35B44)

Related Items (4)

Explicit blowing up solutions for a higher order parabolic equation with Hessian nonlinearity ⋮ Well-posedness and dynamic properties of solutions to a class of fourth order parabolic equation with mean curvature nonlinearity ⋮ Comments on the paper ``Asymptotic behavior for a fourth-order parabolic equation involving the Hessian ⋮ Determination of the time-dependent thermal grooving coefficient

Cites Work

• Unnamed Item
• Unnamed Item
• Ground state sign-changing solutions for Kirchhoff type problems in bounded domains
• The existence and nonexistence results of ground state nodal solutions for a Kirchhoff type problem
• Existence and concentration behavior of positive solutions for a Kirchhoff equation in \(\mathbb R^3\)
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Saddle points and instability of nonlinear hyperbolic equations
• On potential wells and vacuum isolating of solutions for semilinear wave equations
• \(L^{2}\)-norm blow-up of solutions to a fourth order parabolic PDE involving the Hessian
• Global existence versus blow-up results for a fourth order parabolic PDE involving the Hessian
• Some fourth order nonlinear elliptic problems related to epitaxial growth
• Ground state solution for a fourth-order elliptic equation with logarithmic nonlinearity modeling epitaxial growth
• Existence of least energy positive, negative and nodal solutions for a class of \(p \& q\)-problems with potentials vanishing at infinity
• Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains
• Global existence and blow-up for a fourth order parabolic equation involving the Hessian
• On global solution of nonlinear hyperbolic equations
• Solutions for Quasilinear Schrödinger Equations via the Nehari Method
• Dynamic Scaling of Growing Interfaces
• On radial stationary solutions to a model of non-equilibrium growth
• Existence and nonexistence results for a singular boundary value problem arising in the theory of epitaxial growth

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