The title problem is posed as a linear heat equation in one refs. dimension (x greater than 0) and time (t greater than 0), with a nonlinear radiative-type boundary condition on the surface (x equals 0). Existence and uniqueness of a nonnegative solution are shown by a simple, constructive method which leads to some useful bounds. The asymptotic behavior (t yields infinity ) is investigated by a formal expansion scheme. For the case in which the nonlinear boundary condition has an asymptotic power law form, a complete description of the asymptotic behavior is provided. Conservation of flux at the surface (x equals 0) is also determined in this case. For more general nonlinearities, some extreme cases of asymptotic behavior are examined.
|Original language||English (US)|
|Number of pages||17|
|State||Published - Jan 1 1976|
ASJC Scopus subject areas
- Theoretical Computer Science
- Computational Mathematics
- Applied Mathematics