We show existence of a unique, regular global solution of the parabolic-elliptic system $u_t +f(t,x,u)_x+g(t,x,u)+P_x=(a(t,x) u_x)_x$ and $-P_{xx}+P=h(t,x,u,u_x)+k(t,x,u)$ with initial data $u|_{t=0} = u_0$. Here $\inf_{(t,x)}a(t,x)>0$. Furthermore, we show that the solution is stable with respect to variation in the initial data $u_0$ 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.

Wellposedness for a parabolic-elliptic system / Coclite, Giuseppe Maria; Holden, H; Karlsen, K. H.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 13:3(2005), pp. 659-682. [10.3934/dcds.2005.13.659]

Wellposedness for a parabolic-elliptic system

COCLITE, Giuseppe Maria;
2005-01-01

Abstract

We show existence of a unique, regular global solution of the parabolic-elliptic system $u_t +f(t,x,u)_x+g(t,x,u)+P_x=(a(t,x) u_x)_x$ and $-P_{xx}+P=h(t,x,u,u_x)+k(t,x,u)$ with initial data $u|_{t=0} = u_0$. Here $\inf_{(t,x)}a(t,x)>0$. Furthermore, we show that the solution is stable with respect to variation in the initial data $u_0$ 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.
2005
Wellposedness for a parabolic-elliptic system / Coclite, Giuseppe Maria; Holden, H; Karlsen, K. H.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - STAMPA. - 13:3(2005), pp. 659-682. [10.3934/dcds.2005.13.659]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/93835
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