Wellposedness for a Parabolic-elliptic System
نویسندگان
چکیده
We show existence of a unique, regular global solution of the parabolic-elliptic system ut + f(t, x, u)x + g(t, x, u) + 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.
منابع مشابه
Wellposedness of Solutions of a Parabolic-elliptic System
We show existence of a unique, regular global solution of the parabolic-elliptic system ut + f(t, x, u)x + g(t, x, u) + 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...
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