Title
A free boundary value problem related to the combustion of a solid: Flux boundary conditions
Abstract
We demonstrate the existence, uniqueness, and continuous dependence upon the data for the solution (u, v, s) of the free boundary value problem: vt = αuxx, vt = βvxx, 0 < x < s(t), 0 < t ≤ T, u(x, 0) = φ(x), v(x, 0) = ψ(x), 0 ≤ x ≤ s(0) = b. -αux(0, t) = f(t), -βvx(0, t) = g(t), 0 < t ≤ T, αux(s(t), t) = -(γ + u(s(t), t))ṡ(t), βvx(s(t), t) = (μ - v(s(t), t))ṡ(t), 0 < t ≤ T, ṡ(t) = v(u(s(t), t)) exp(-δ/v(s(t), t))F(u(s(t), t)), 0 < t ≤ T, where α, β, γ, δ, and μ are positive constants related to the physical constants.
Publication Date
1-1-1997
Publication Title
Quarterly of Applied Mathematics
Volume
55
Issue
4
Number of Pages
687-705
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1090/qam/1486543
Copyright Status
Unknown
Socpus ID
0031399017 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/0031399017
STARS Citation
Cannon, John R. and Matheson, Alec L., "A free boundary value problem related to the combustion of a solid: Flux boundary conditions" (1997). Scopus Export 1990s. 2751.
https://stars.library.ucf.edu/scopus1990/2751