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
Source: 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":
\[
\begin{cases}
C\frac{\partial u}{\partial t}-k\frac{\partial^{2}u}{\partial x^{2}}=0,0u(0,t)=h(t),u(1,t)=h(t),\\
u(x,0)=u(x),s(0)=s_{0},\\
s(0)=s_{0},k\left[\frac{\partial u(s(t)+,t)}{\partial x}-\frac{\partial u(s(t)-,t)}{\partial x}\right]=L\dot{s(t)=} & Lg(u(s(t),t))
\end{cases}
\]
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:
\[
\begin{cases}
C\frac{\partial u}{\partial t}-k\frac{\partial^{2}u}{\partial x^{2}}=0,0u(0,t)=h(t),u(1,t)=h(t),\\
u(x,0)=u(x),s(0)=s_{0},\\
s(0)=s_{0},k\left[\frac{\partial u(s(t)+,t)}{\partial x}-\frac{\partial u(s(t)-,t)}{\partial x}\right]=L\dot{s(t)=} & Lg(u(s(t),t))
\end{cases}
\]
and prove the existence of its weak or classical solutions under some
conditions.
Type: Article
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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