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Exact Solutions of Hyperbolic Reaction-Diffusion Equations in Two Dimensions

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posted on 2023-12-01, 00:57 authored by Philip BroadbridgePhilip Broadbridge, J Goard
Exact solutions are constructed for a class of nonlinear hyperbolic reaction-diffusion equations in two-space dimensions. Reduction of variables and subsequent solutions follow from a special nonclassical symmetry that uncovers a conditionally integrable system, equivalent to the linear Helmholtz equation. The hyperbolicity is commonly associated with a speed limit due to a delay, between gradients and fluxes. With lethal boundary conditions on a circular domain wherein a species population exhibits logistic growth of Fisher-KPP type with equal time lag, the critical domain size for avoidance of extinction does not depend on. A diminishing exact solution within a circular domain is also constructed, when the reaction represents a weak Allee effect of Huxley type. For a combustion reaction of Arrhenius type, the only known exact solution that is finite but unbounded is extended to allow for a positive.

History

Publication Date

2022-10-01

Journal

Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal

Volume

64

Issue

4

Pagination

17p. (p. 338-354)

Publisher

Cambridge University Press

ISSN

1446-1811

Rights Statement

© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.

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