scholarly journals A Liouville Theorem for Superlinear Heat Equations on Riemannian Manifolds

2019 ◽  
Vol 87 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Daniele Castorina ◽  
Carlo Mantegazza ◽  
Berardino Sciunzi
Keyword(s):  
Riemannian Manifolds ◽  
Liouville Theorem ◽  
Heat Equations

scholarly journals Ancient solutions of superlinear heat equations on Riemannian manifolds

2020 ◽  
pp. 2050033
Author(s):  
Daniele Castorina ◽  
Carlo Mantegazza
Keyword(s):  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Heat Equations ◽  
Qualitative Properties ◽  
Ancient Solutions

We study some qualitative properties of ancient solutions of superlinear heat equations on a Riemannian manifold, with particular interest in positivity and constancy in space.

scholarly journals A matrix Harnack inequality for semilinear heat equations

2022 ◽  
Vol 5 (1) ◽  
pp. 1-15
Author(s):  
Giacomo Ascione ◽  
◽  
Daniele Castorina ◽  
Giovanni Catino ◽  
Carlo Mantegazza ◽  
...  
Keyword(s):  
Heat Equation ◽  
Positive Solutions ◽  
Harnack Inequality ◽  
Riemannian Manifolds ◽  
Ricci Tensor ◽  
Heat Equations ◽  
Standard Heat ◽  
Matrix Version ◽  
Sectional Curvatures ◽  
Parallel Ricci Tensor

<abstract><p>We derive a matrix version of Li &amp; Yau–type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parallel Ricci tensor, similarly to what R. Hamilton did in <sup>[<xref ref-type="bibr" rid="b5">5</xref>]</sup> for the standard heat equation. We then apply these estimates to obtain some Harnack–type inequalities, which give local bounds on the solutions in terms of the geometric quantities involved.</p></abstract>

THE LIOUVILLE THEOREM INVOLVING QUANTUM EFFECT

1986 ◽  
Vol 6 (2) ◽  
pp. 201-211 ◽  
Author(s):  
Keda Bao ◽  
Fusui Liu
Keyword(s):  
Liouville Theorem ◽  
Quantum Effect
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