On the transition from initial data to travelling waves in the Fisher-KPP equation
UNSPECIFIED. (1998) On the transition from initial data to travelling waves in the Fisher-KPP equation. DYNAMICS AND STABILITY OF SYSTEMS, 13 (2). pp. 167-174. ISSN 0268-1110Full text not available from this repository.
The Fisher-KPP equation u(t) = u(xx) + u(1 - u) has a travelling wave solution for all speeds greater than or equal to 2. Initial data that decrease monotonically from 1 to 0 on - infinity < x < infinity, with u(x, 0) = O-s(e(-Ex)) as x --> infinity, are Known to evolve to a travelling wave, whose speed depends on zeta. Here, it is shown that the relationship between wave speed and zeta can be recovered by linearizing the Fisher-KPP equation about u = O and explicitly, solving the linear equation. Moreover, the calculation predicts that in the case zeta > I, the solution for u,iu itself evolves to a transition wave, moving ahead of the (minimum speed) u wave at the greater speed of 2 zeta. Behind this transition, u(x)/u = - x/(2t), while ahead of it, u,iu = - zeta The paper goes on to discuss the potential applications of the method to systems of coupled reaction-diffusion equations.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics
T Technology > TJ Mechanical engineering and machinery
|Journal or Publication Title:||DYNAMICS AND STABILITY OF SYSTEMS|
|Publisher:||CARFAX PUBL CO|
|Number of Pages:||8|
|Page Range:||pp. 167-174|
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