scholarly journals A note on time analyticity for ancient solutions of the heat equation

2019 ◽  
Vol 148 (4) ◽  
pp. 1665-1670 ◽  
Author(s):  
Qi S. Zhang
Keyword(s):  
Heat Equation ◽  
Ancient Solutions

scholarly journals On Ancient Solutions of the Heat Equation

2019 ◽  
Vol 72 (9) ◽  
pp. 2006-2028 ◽  
Author(s):  
Fanghua Lin ◽  
Q. S. Zhang
Keyword(s):  
Heat Equation ◽  
Ancient Solutions

scholarly journals Entire and ancient solutions of a supercritical semilinear heat equation

2021 ◽  
Vol 41 (1) ◽  
pp. 413-438
Author(s):  
Peter Poláčik ◽  
◽  
Pavol Quittner ◽  
Keyword(s):  
Heat Equation ◽  
Semilinear Heat Equation ◽  
Ancient Solutions

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

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