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

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Clark, V.¹  Meyer, J. C.² 

[1] Univ Exeter, Coll Engn Math & Phys Sci, Exeter, Devon, England

[2] Univ Birmingham, Sch Math, Watson Bldg, Birmingham, W Midlands, England

关键词: Semi-linear parabolic PDE;    Well-posedness;    Oscillation;    Non-Lipschitz;    Self-similar solutions;   

DOI  :  10.1016/j.jde.2020.01.007

来源: Elsevier

【 摘 要 】

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 eta -> infinity. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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