Self-similar asymptotics of solutions to heat equation with inverse square potential

DOI10.1007/s00028-012-0169-8zbMath1263.35149OpenAlexW1994833108MaRDI QIDQ1945690

Dominika Pilarczyk

Publication date: 8 April 2013

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-012-0169-8

zbMATH Keywords

large-time asymptoticssingular potential

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Heat equation (35K05) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for second-order parabolic equations (35K15) Singular parabolic equations (35K67) Self-similar solutions to PDEs (35C06)

Related Items (12)

Critical dissipative estimate for a heat semigroup with a quadratic singular potential and critical exponent for nonlinear heat equations ⋮ Self-similar solution for Hardy operator ⋮ Self-similarity in homogeneous stationary and evolution problems ⋮ Relativistic stable operators with critical potentials ⋮ Existence of solutions to heat equations with singular lower order terms ⋮ Around a singular solution of a nonlocal nonlinear heat equation ⋮ Fractional Laplacian with Hardy potential ⋮ Mathematical challenges in the theory of chemotaxis ⋮ Asymptotic behaviour for elliptic operators with second-order discontinuous coefficients ⋮ Probabilistic approach to the heat equation with a dynamic Hardy-type potential ⋮ Variation operators associated with the semigroups generated by Schrödinger operators with inverse square potentials ⋮ Hardy inequalities and non-explosion results for semigroups

Cites Work

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• Schrödinger semigroups
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• On semigroups generated by left-invariant positive differential operators on nilpotent Lie groups
• Parabolic Harnack inequality for the heat equation with inverse-square potential
• Global bounds of Schrödinger heat kernels with negative potentials

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