Square root of absolute value of derivative on a segment

Abstract

We consider the initial-boundary-value problem for a nonlinear pseudodifferential equation on a segment. We are interested in the case of a nonanalytic symbol of the pseudodifferential operator $K(p)=\sqrt{\left\vert p\right\vert }.$ We study traditionally important problems of the theory of nonlinear partial differential equations, such as global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behavior of solutions for large time.