Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
arXiv:2111.02753 · doi:10.57262/die036-0910-727
Abstract
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 behaviour 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 generalisations on Euclidean space. The main tools in our analysis are the Fourier transform and spectral methods.
arXiv comment22 pages
References in corpus (10)
- Boundary representations of operator spaces, and compact rectangular matrix convex sets
- Eventually Positive Semigroups of Linear Operators
- Eventually and asymptotically positive semigroups on Banach lattices
- Bi-Laplacians on graphs and networks
- A criterion for the uniform eventual positivity of operator semigroups
- The Bi-Laplacian with Wentzell boundary conditions on Lipschitz domains
- The role of domination and smoothing conditions in the theory of eventually positive semigroups
- Locally Eventually Positive Operator Semigroups
- Schrödinger and polyharmonic operators on infinite graphs: Parabolic well-posedness and p-independence of spectra
- Spectrum and convergence of eventually positive operator semigroups