| Abstract |
We establish local well-posedness in Sobolev spaces H-s(T), with s >= -1/2, for the initial value problem issues of the equation u(t) + u(xxx) + eta Lu + uu(x) = 0, x is an element of T, t >= 0, where eta > 0, (Lu)boolean AND(k) = -Phi(k)(u) over cap (k), k is an element of and Phi is an element of R is bounded above. Particular cases of this problem are the Korteweg-de Vries-Burgers equation for Phi(k) = -k(2), the derivative Korteweg-de Vries-Kuramoto-Sivashinsky equation for Phi(k) = k(2) - k(4), and the Ostrovsky-Stepanyams-Tsimring equation for Phi(k) = vertical bar k vertical bar - vertical bar k vertical bar(3). |
