#### Title

A Free Boundary Value Problem Related To The Combustion Of A Solid: Flux Boundary Conditions

#### Title - Alternative

Q. Appl. Math.

#### Keywords

Mathematics, Applied

#### Abstract

We demonstrate the existence, uniqueness, and continuous dependence upon the data for the solution (u, v, s) of the free boundary value problem: u(t) = alpha U-xx, v(t) = beta v(xx), 0 < x < s(t), 0 < t less than or equal to T, u(x, 0) = phi(x), v(x, 0) = psi(x), 0 less than or equal to x less than or equal to s(0) = b. -alpha u(x)(0, t) = f(t), -beta v(x)(0, t) = g(t), 0 < t less than or equal to T, alpha u(x)(s(t), t) = -(gamma + u(s(t), t))(s) over dot (t), beta v(x)(s(t), t) = (mu - v(s(t), t))(s) over dot (t), 0 < less than or equal to T, (s) over dot (t) = nu(v(s(t), t)) exp(-delta/v(s(t), t))F(u(s(t), t)), 0 < t < T, where alpha, beta, gamma, delta, and mu, are positive constants related to the physical constants.

#### Publication Title

Quarterly of Applied Mathematics

#### Volume

55

#### Issue/Number

4

#### Publication Date

1-1-1997

#### Document Type

Article

#### Language

English

#### First Page

687

#### Last Page

705

#### WOS Identifier

WOS:000071266600006

#### ISSN

0033-569X

#### Recommended Citation

Cannon, J. R. and Matheson, A. L., "A Free Boundary Value Problem Related To The Combustion Of A Solid: Flux Boundary Conditions" (1997). *Faculty Bibliography*. 1868.

http://stars.library.ucf.edu/facultybib/1868