论文信息 - Singularly perturbed telegraph equations with applications in the random walk theory

Singularly perturbed telegraph equations with applications in the random walk theory

In the paper we analyze singularly perturbed telegraph systems applying the newly developed compressed asymptotic method and show that the diffusion equation is an asymptotic limit of singularly perturbed telegraph system of equations. The results are applied to the random walk theory for which the relationship between correlated and uncorrelated random walks is explained in asymptotic terms.

Jacek Banasiak | Janusz R. Mika | J. Mika | J. Banasiak

[1] S. Goldstein. ON DIFFUSION BY DISCONTINUOUS MOVEMENTS, AND ON THE TELEGRAPH EQUATION , 1951 .

[2] Asymptotic analysis of the linear Boltzmann equation with and without an external field: Comparison of various approaches , 1997 .

[3] J. Mika,et al. Asymptotic analysis of singularly perturbed systems of ordinary differential equations , 1991 .

[4] Asymptotic equivalence of the P1 and diffusion equations , 1978 .

[5] M. Kac. A stochastic model related to the telegrapher's equation , 1974 .

[6] Geoffrey Ingram Taylor,et al. Diffusion by Continuous Movements , 1922 .

[7] New asymptotic expansion algorithm for singularly perturbed evolution equations , 1981 .

[8] Diffusion limit for a linear kinetic equation , 1995 .

[9] Diffusion limit for the linear boltzmann equation of the neutron transport theory , 1994 .

[10] A. Janssen. The distance between the Kac process and the Wiener process with applications to generalized telegraph equations , 1990 .