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A matrix Harnack inequality for semilinear heat equations

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 نشر من قبل Giovanni Catino
 تاريخ النشر 2021
  مجال البحث
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We derive a matrix version of Li & 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~cite{hamilton7} 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.



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