Type: Article

Neumann problem for nonlinear Schrödinger equation with the Riesz fractional derivative operator

Esquivel, L; Kaikina, E.;

Abstract:

We consider the initial–boundary value problem for the fractional Schrödinger equation, posed on positive half-line x>0x>0: View the MathML source{ut+iuxx+i|u|2u+|?x|12u=0,t?0,x?0;u(x,0)=u0(x),x>0,ux(0,t)=h(t),t>0, where View the MathML source|?x|12 is the fractional derivative operator defined by the Riesz potential View the MathML source|?x|12=12??0?sign(x?y)|x?y|uy(y)dy. We study the global existence in time and asymptotics of solutions to the initial–boundary value problema.