Classification of  local asymptoticsfor solutions to heat equations withinverse-square potentials

Veronica Felli; Ana Primo

doi:10.3934/dcds.2011.31.65

Article Contents

2011, Volume 31, Issue 1: 65-107. Doi: 10.3934/dcds.2011.31.65

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Classification of local asymptotics for solutions to heat equations with inverse-square potentials

Veronica Felli^1, and
Ana Primo^2,

1.
Università di Milano Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano
2.
ICMAT, Instituto de Ciencias Matemáticas, Campus Cantoblanco, Calle Nicolás Cabrera 13–15, 28049 Madrid

Received: February 28, 2010

Revised: October 31, 2010

Published: December 2010

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Abstract

Asymptotic behavior of solutions to heat equations with spatially singular inverse-square potentials is studied. By combining a parabolic Almgren type monotonicity formula with blow-up methods, we evaluate the exact behavior near the singularity of solutions to linear and subcritical semilinear parabolic equations with Hardy type potentials. As a remarkable byproduct, a unique continuation property is obtained.

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Mathematics Subject Classification: 35K67, 35K58, 35B40.

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