On two-signed solutions to a second order semi-linear parabolic partial differential equation with non-Lipschitz nonlinearity

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  • University of Exeter


In this paper, we establish the existence of a 1-parameter family of spatially inhomogeneous radially symmetric classical self-similar solutions to a Cauchy problem for a semi-linear parabolic PDE with non-Lipschitz nonlinearity and trivial initial data. Specifically we establish well-posedness for an associated initial value problem for a singular two-dimensional non-autonomous dynamical system with non-Lipschitz nonlinearity. Additionally, we establish that solutions to the initial value problem converge algebraically to the origin and oscillate as η→∞.


Original languageEnglish
Pages (from-to)1401-1431
Number of pages31
JournalJournal of Differential Equations
Issue number2
Early online date15 Jan 2020
Publication statusPublished - 5 Jul 2020


  • semi-linear parabolic PDE, well-posedness, oscillation, non-Lipschitz, Self-similar solutions, Oscillation, Semi-linear parabolic PDE, Non-Lipschitz, Well-posedness

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