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

    Authors

    J. R. Cannon;A. L. Matheson

    Comments

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    Abbreviated Journal Title

    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.

    Journal 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

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