The Kawahara equation on bounded intervals and on a half-line

We consider an initial–boundary value problem for the Kawahara equation posed on bounded intervals and on a half-line. We prove the existence and uniqueness of global regular and weak solutions on bounded intervals (0,L)(0,L) as well as a priori estimates which do not depend on LL and prove that regular and weak solutions on bounded intervals converge to regular and weak solutions on the positive half-line as L→∞L→∞.