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Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4834

Title: Existence of solutions to the problem of nonequilibrium phase change
Authors: Zhicheng, Guan
Issue Date: 1989
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: Guan Zhicheng, “Existence of solutions to the problem of nonequilibrium phase change”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 21 (1989), pp. 39-50.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
21 (1989)
Abstract: In questo lavoro si considera il seguente problema di "nonequilibrium phase-change": \[ \begin{cases} C\frac{\partial u}{\partial t}-k\frac{\partial^{2}u}{\partial x^{2}}=0,0<x<1,0<t<T,\\ u(0,t)=h(t),u(1,t)=h(t),\\ u(x,0)=u(x),s(0)=s_{0},\\ s(0)=s_{0},k\left[\frac{\partial u(s(t)+,t)}{\partial x}-\frac{\partial u(s(t)-,t)}{\partial x}\right]=L\dot{s(t)=} & Lg(u(s(t),t)) \end{cases} \] e si dimostra l'esistenza di sue soluzioni deboli o classiche sotto certe condizioni.
In thls paper we consider the following problem of nonequilibrlum phase-change: \[ \begin{cases} C\frac{\partial u}{\partial t}-k\frac{\partial^{2}u}{\partial x^{2}}=0,0<x<1,0<t<T,\\ u(0,t)=h(t),u(1,t)=h(t),\\ u(x,0)=u(x),s(0)=s_{0},\\ s(0)=s_{0},k\left[\frac{\partial u(s(t)+,t)}{\partial x}-\frac{\partial u(s(t)-,t)}{\partial x}\right]=L\dot{s(t)=} & Lg(u(s(t),t)) \end{cases} \] and prove the existence of its weak or classical solutions under some conditions.
URI: http://hdl.handle.net/10077/4834
ISSN: 0049-4704
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.21 (1989)

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