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Asymptotic relationship between telegraphic and diffusion equations
Author(s) -
Mika J.,
Stankiewicz R.,
Neunzert H.
Publication year - 1981
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670030104
Subject(s) - mathematics , zero (linguistics) , diffusion equation , diffusion , mathematical analysis , mathematical physics , physics , thermodynamics , philosophy , linguistics , economy , economics , service (business)
Abstract In the paper it is considered the generalized telegraphic equation represented by the system of four evolution equations, containing a small positive parameter multiplying some of the time derivatives. It is shown that if the small parameter tends to zero, the solution to the telegraphic equation tends asymptotically to the solution of the diffusion equation obtained from the former one by putting the small parameter equal to zero.