Local existence for a general model of size-dependent population dynamics.
Kato, Nobuyuki, Torikata, Hiroyuki (1997)
Abstract and Applied Analysis
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Local existence for a general model of size-dependent population dynamics.
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This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate...