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- W2081330362 abstract "INTRODUCTION IN THIS paper we study the Volterra diffusion equation au/at = Au + au bu2 u(f*u)t (0.1 a) describing the evolution of some population governed by the intrinsic rate a bu and the memory rate f * u containing the effect of the past history on the actual population development. We suppose that the population lives in some bounded domain Sz without interaction with the exterior situation; this is expressed by the Neumann condition au/&i = 0 on aR (0.1 b) where Z%2 is the boundary of R and a/an is the exterior normal derivative to X?. Moreover we consider the initial condition u(x, 0) = UJX) > 0. (0.1 c) Let us observe that the classical Volterra equation [2] : ti = au bu2 u(f * u), u(O) = u. = const. (0.2) is equivalent to problem (0.1) with homogeneous initial distribution. [3] with the following hypoA discussion of problem (0.2) is contained, for instance, in theses [2] and" @default.
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- W2081330362 date "1979-08-01" @default.
- W2081330362 modified "2023-10-01" @default.
- W2081330362 title "On a diffusion volterra equation" @default.
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- W2081330362 doi "https://doi.org/10.1016/0362-546x(79)90088-9" @default.
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