On two-signed solutions to a second order semi-linear parabolic partial differential equation with non-Lipschitz nonlinearity
Research output: Contribution to journal › Article
Colleges, School and Institutes
- 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→∞.
|Journal||Journal of Differential Equations|
|Early online date||15 Jan 2020|
|Publication status||E-pub ahead of print - 15 Jan 2020|