Differential and Integral Equations

On a class of critical heat equations with an inverse square potential

Pigong Han and Zhaoxia Liu

Full-text: Open access


In this paper, we study a class of parabolic equations with critical Sobolev exponents and Hardy terms. Using Moser-type iteration, we characterize the asymptotic behavior of solutions at singular points. By means of critical point theory and the potential well method, we prove both global existence and finite-time blow-up depending on the initial datum.

Article information

Differential Integral Equations, Volume 20, Number 1 (2007), 27-50.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K55: Nonlinear parabolic equations
Secondary: 35B40: Asymptotic behavior of solutions 35K20: Initial-boundary value problems for second-order parabolic equations 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)


Liu, Zhaoxia; Han, Pigong. On a class of critical heat equations with an inverse square potential. Differential Integral Equations 20 (2007), no. 1, 27--50. https://projecteuclid.org/euclid.die/1356050278

Export citation