A minimization problem related to the estimation of a lower bound for the temperature in a free boundary value problem related to the combustion of a solid |
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Authors: | John R Cannon Chung-Chiang Chou Alec L Matheson |
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Institution: | 1. Lamar University, 77710, Beaumont, TX, USA
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Abstract: | This paper investigates the least time τ* of the first zero of the bounded solution to an initial boundary value problem for the heat equation. The heat equation is considered in the domain $$\left\{ {(x,t)| - \infty< x< s(t),0< t \leqslant T} \right\}$$ . The initial conditionu(x, 0)=φ(x) and the boundary conditionu x (s(t),t)=?R are specified. Let τ=τ(φ,R, s) denote the first zero ofu onx=s(t), that is,u(s(τ), τ)=0. Let τ*=min τ, where the minimum is taken over a class of functionss=s(t). The existence of τ* is demonstrated, and a generalization of the problem is discussed. |
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