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Travelling fronts in the diffusive Nicholson’s blowflies equation with distributed delays. (English) Zbl 0969.35133
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 $u= \ln\beta$. The existence of such travelling solutions is proved when $f(t)$ assumes a special form; some qualitative properties of these solutions are established.

35R10Partial functional-differential equations
35K55Nonlinear parabolic equations
Full Text: DOI
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