Parabolic Behavior of a Hyperbolic Delay Equation

نویسندگان

Thomas Laurent

Brian Rider

Michael Reed

چکیده

It is shown that the fundamental solution of a hyperbolic partial differential equation with time delay has a natural probabilistic structure, i.e. is approximately Gaussian, as t → ∞. The proof uses ideas from the DeMoivre proof of the Central Limit Theorem. It follows that solutions of the hyperbolic equation look approximately like solutions of a diffusion equation with constant convection as t→∞.

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