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.
Felli, V., PRIMO RAMOS, A. (2011). Classification of local asymptotics for solutions to heat equations with inverse-square potentials. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 31(1), 65-107 [10.3934/dcds.2011.31.65].
Classification of local asymptotics for solutions to heat equations with inverse-square potentials
FELLI, VERONICA;PRIMO RAMOS, ANA
2011
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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