Some new properties of biharmonic heat kernels

DOI10.1016/j.na.2008.12.039zbMath1170.35440OpenAlexW2037063404MaRDI QIDQ1017730

Hans-Christoph Grunau, Gazzola, Filippo

Publication date: 12 May 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.12.039

zbMATH Keywords

heat kernelsbiharmonic parabolic equationshigher-order polyharmonic parabolic problemsLorch-Szegő-type monotonicity resultspositivity results

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for higher-order parabolic equations (35K30)

Related Items (11)

The polyharmonic heat flow of closed plane curves ⋮ On the biharmonic heat equation on complete Riemannian manifolds ⋮ On the curve diffusion flow of closed plane curves ⋮ Biharmonic Fick-Jacobs diffusion in narrow channels ⋮ Wide oscillation finite time blow up for solutions to nonlinear fourth-order differential equations ⋮ An asymptotic study of blow up multiplicity in fourth order parabolic partial differential equations ⋮ \(L^p\) estimates for the Schrödinger type operators ⋮ On the well-posedness for a class of pseudo-differential parabolic equations ⋮ On the very weak solvability of the beam equation ⋮ On the eventual local positivity for polyharmonic heat equations ⋮ Finite time blow-up of complex solutions of the conserved Kuramoto–Sivashinsky equation in ℝ^d and in the torus 𝕋^d, d ⩾ 1

Cites Work

• Unnamed Item
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• Eventual local positivity for a biharmonic heat equation in \(\mathbb R^n\)
• Decay and local eventual positivity for biharmonic parabolic equations
• On the sign of solutions to some linear parabolic biharmonic equations
• Higher monotonicity properties of certain Sturm-Liouville functions
• Existence and nonexistence of global solutions of higher-order parabolic problems with slow decay initial data
• Global solutions of higher-order semilinear parabolic equations in the supercritical range
• Global solutions for superlinear parabolic equations involving the biharmonic operator for initial data with optimal slow decay
• Existence and blow-up for higher-order semilinear parabolic equations: Majorizing order-preserving operators

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