LOCAL UNIFORM CONVERGENCE AND EVENTUAL POSITIVITY OF SOLUTIONS TO BIHARMONIC HEAT EQUATIONS

被引：2
|
作者：
Daners, Daniel [1 ]
Glueck, Jochen [2 ,3 ]
Mui, Jonathan [1 ]
机构：
[1] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia
[2] Univ Passau, Innstr 41, D-94032 Passau, Germany
[3] Univ Wuppertal, Sch Math & Nat Sci, Gaussstr 20, D-42119 Wuppertal, Germany
来源：
DIFFERENTIAL AND INTEGRAL EQUATIONS | 2023年 / 36卷 / 9-10期
关键词：
SEMIGROUPS;
D O I：
10.57262/die036-0910-727
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus is on the asymptotic behavior and positivity properties of the solutions for large times. In particular, we derive the local eventual positivity of solutions. We furthermore prove the local eventual positivity of solutions to the biharmonic heat equation and its generalizations on Euclidean space. The main tools in our analysis are the Fourier transform and spectral methods.
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页码：727 / 756
页数：30
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