Singularity Formation in Chemotaxis--- A Conjecture of Nagai
In: SIAM Journal on Applied Mathematics, Jg. 65 (2004), S. 336-360
Online
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Zugriff:
Consider the initial-boundary value problem for the system (S)ut = uxx - (uvx)x, vt= u- av on an interval [0,1] for t > 0, where a > 0 with ux(0,t) = ux(1,t)= 0. Suppose \mu, v0 are positive constants. The corresponding spatially homogeneous global solution U(t) = \mu, V(t) = \mu a + (v0 - \mu a)\exp(-at) is stable in the sense that if (\mu',v0' ) are positive constants, the corresponding spatially homogeneous solution will be uniformly close to (U(\cdot),V(\cdot)).We consider, in sequence space, an approximate system (S') which is related to (S) in the following sense: The chemotactic term (uvx)x is replaced by the inverse Fourier transform of the finite part of the convolution integral for the Fourier transform of (uvx)x. (Here the finite part of the convolution on the line at a point x of two functions, f,g, is defined as $\int_0^x(f(y)g(y-x)\,dy$.) We prove the following: If \mu > a, then in every neighborhood of (\mu,v0 ) there are (spatially nonconstant) initial data for which the solution of proble...
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Singularity Formation in Chemotaxis--- A Conjecture of Nagai
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Autor/in / Beteiligte Person: | Renclawowicz, Joanna ; Levine, Howard A. |
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Zeitschrift: | SIAM Journal on Applied Mathematics, Jg. 65 (2004), S. 336-360 |
Veröffentlichung: | Society for Industrial & Applied Mathematics (SIAM), 2004 |
Medientyp: | unknown |
ISSN: | 1095-712X (print) ; 0036-1399 (print) |
DOI: | 10.1137/s0036139903431725 |
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