On Ancient Solutions of the Heat Equation
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Publication:5243674
DOI10.1002/cpa.21820zbMath1461.35098arXiv1712.04091OpenAlexW2963018951MaRDI QIDQ5243674
Publication date: 19 November 2019
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.04091
Heat equation (35K05) Integral representations of solutions to PDEs (35C15) Initial value problems for second-order parabolic equations (35K15) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53) PDEs on manifolds (35R01)
Related Items (24)
Complexity of parabolic systems ⋮ Polynomial growth ancient solutions to harmonic form heat flow ⋮ Time analyticity of the biharmonic heat equation, the heat equation with potentials and some nonlinear heat equations ⋮ Time analyticity for the heat equation and Navier-Stokes equations ⋮ Ancient solutions to nonlocal parabolic equations ⋮ Differential Harnack inequalities for semilinear parabolic equations on Riemannian manifolds. I: Bakry-Émery curvature bounded below ⋮ Differential Harnack inequalities for semilinear parabolic equations on \(\mathrm{RCD}^{\ast} (K,N)\) metric measure spaces ⋮ Liouville theorems for ancient solutions to the \(V\)-harmonic map heat flows ⋮ Harmonic and Schrödinger functions of polynomial growth on gradient shrinking Ricci solitons ⋮ Evolution of form and shape ⋮ Harmonic functions of polynomial growth on infinite penny graphs ⋮ Unique continuation problem on RCD spaces. I ⋮ Time analyticity for the parabolic type Schrödinger equation on Riemannian manifold with integral Ricci curvature condition ⋮ Time regularity for local weak solutions of the heat equation on local Dirichlet spaces ⋮ Time analyticity for inhomogeneous parabolic equations and the Navier-Stokes equations in the half space ⋮ Liouville theorems for ancient caloric functions via optimal growth conditions ⋮ Lipschitz property of bistable or combustion fronts and its applications ⋮ Discrete harmonic functions on infinite penny graphs ⋮ Blow-ups of caloric measure in time varying domains and applications to two-phase problems ⋮ A note on time analyticity for ancient solutions of the heat equation ⋮ Gradient estimates for a class of semilinear parabolic equations and their applications ⋮ Time analyticity of solutions to the heat equation on graphs ⋮ Optimal bounds for ancient caloric functions ⋮ Sharp gradient estimates for a heat equation in Riemannian manifolds
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