Abstract:We show existence of a unique, regular global solution of the parabolic-elliptic systemu_{t}+f(t,x,u)_{x}+g(t,x,u)_{x}+P_{x}=(a(t,x)u_{x})_{x}and −P_{xx}+P=h(t,x,u,u_{x})+k(t,x,u) with initial datau|_{t=0}=u_{0}. Here inf_{(t,x)}a(t,x)>0. Furthermore, we show that the solution is stable with respect to variation in the initial datau_{0}and the functionsf,getc. Explicit stability estimates are provided. The regularized generalized Camassa–Holm equation is a special case of the model we discuss.

**Paper:**- Available as PDF (272 Kbytes), Postscript (1184 Kbytes) or gzipped PostScript (328 Kbytes; uncompress using gunzip).
**Author(s):**- Giuseppe M. Coclite <giusepc@math.uio.no>
- Helge Holden, <holden@math.ntnu.no>
- Kenneth H. Karlsen, <kennethk@math.uio.no>
**Publishing information:****Comments:****Submitted by:**- <giusepc@math.uio.no> January 28 2005.

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Conservation Laws Preprint Server <conservation@math.ntnu.no> 2005-02-02 13:24:16 UTC