Preprint 2005-007

Wellposedness for a parabolic-elliptic system

Giuseppe M. Coclite, Helge Holden and Kenneth H. Karlsen

Abstract: We show existence of a unique, regular global solution of the parabolic-elliptic system ut+f(t,x,u)x+g(t,x,u)x+Px=(a(t,x)ux)x and Pxx+P=h(t,x,u,ux)+k(t,x,u) with initial data u|t=0=u0. Here inf(t,x)a(t,x)>0. Furthermore, we show that the solution is stable with respect to variation in the initial data u0 and the functions f, g etc. Explicit stability estimates are provided. The regularized generalized Camassa–Holm equation is a special case of the model we discuss.

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Giuseppe M. Coclite <>
Helge Holden, <>
Kenneth H. Karlsen, <>
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<> January 28 2005.

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