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

Socpus ID

0031399017 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0031399017

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