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

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


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