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Zbl 0969.35133
Gourley, S.A.
Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays. (English)
[J] Math. Comput. Modelling 32, No.7-8, 843-853 (2000). ISSN 0895-7177

The author considers some equations of the form $$\partial u/\partial t= \partial^2u/\partial x^2- u+\beta(f* u) e^{-(f* u)},$$ where $(f* u)(x, t)= \int^t_{-\infty} f(t- s)u(x, s) ds$ (the kernel $f: [0,\infty)\to [0,\infty)$ satisfies: $f(t)\ge 0$, $\forall t\ge 0$ and $\int^\infty_0 f(t) dt= 1$) and $\beta> 1$ is a parameter. He seeks travelling wave front solutions $u(x, t)= U(z)$, $z= x-ct$, $c>0$, in connection with the steady state solutions $u=0$ and $u= \ln\beta$.\par The existence of such travelling solutions is proved when $f(t)$ assumes a special form; some qualitative properties of these solutions are established.
[Ion Onciulescu (Iaşi)]

MSC 2000:: *35R10 Difference-partial differential equations
92D40 Ecology
35K55 Nonlinear parabolic equations

Keywords: travelling wave front solutions; existence; properties

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Zentralblatt MATH Berlin [Germany]