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

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

2010-02-18

arxiv.org/abs/1002.3566v1

Mathematics

Analysis of PDEs

Scientific paper

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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