Coclite, Giuseppe Maria; Holden, Helge; Karlsen, Kenneth Hvistendahl Wellposedness for a parabolic-elliptic system. (English) Zbl 1082.35056 Discrete Contin. Dyn. Syst. 13, No. 3, 659-682 (2005). The authors study a system that constitutes a generalized and regularized Camassa-Holm equation, that is \[ \begin{aligned} &u_t+ (f(t,x,u))_x+ g(t,x,u)+ P_x= (a(t,x)u_x)_x,\\ &-P_{xx}+P= h(t,x,u,u_x)+ \kappa(t,x,u), \quad u|_{t=0}= u_0(x), \end{aligned} \tag{1} \] on the domain \((t,x)\in Q_T:= [0,t]\times \mathbb R\). The authors address the question of wellposedness of the system (1). In particular, they focus on stability of solutions with respect to variation not only in the initial data, but also variation with respect to the functions \(f,a\). Moreover, the authors are interested in the vanishing viscosity limit of (1), that is, when \(a\to 0\). Reviewer: Messoud A. Efendiev (Berlin) Cited in 2 ReviewsCited in 74 Documents MSC: 35G25 Initial value problems for nonlinear higher-order PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:Camassa-Holm equation; dynamical and structural stability PDFBibTeX XMLCite \textit{G. M. Coclite} et al., Discrete Contin. Dyn. Syst. 13, No. 3, 659--682 (2005; Zbl 1082.35056) Full Text: DOI