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Asymptotic periodicity of the Volterra equation with infinite delay. (English) Zbl 1133.35004
Asymptotic periodic properties are obtained for special Volterra delay differential equations. As an example the following equation is considered
\[ \begin{alignedat}{2} \frac{\partial u}{\partial t}-\frac{\partial^2 u}{\partial x^2} &= u\left[ a-bu-c\int^{\infty}_{0}u(t-\tau,x)\,d\mu(\tau)\right], &\quad &(t,x)\in (0,\infty)\times (0,1),\\ u(t,0)&= u(t,1)=0, &\quad &t\in (0,\infty),\\ u(t,x)&=\varphi(t,x), &\quad &(t,x)\in (-\infty,0]\times[0,1]. \end{alignedat} \]

35B10 Periodic solutions to PDEs
35B40 Asymptotic behavior of solutions to PDEs
35R10 Partial functional-differential equations
45K05 Integro-partial differential equations
Full Text: DOI
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