Generalized solutions to mixed problem in half-strip for the Korteweg-de~Vries equation (Q2719508)

The author studies a mixed problem in the half-strip \(\Pi_T^+ = (0,T)\times \mathbb{R}_+\) for the Korteweg-de~Vries equation NEWLINE\[NEWLINE u_t+u_{xxx}+au_x+uu_x=f(t,x)NEWLINE\]NEWLINE with the initial condition NEWLINE\[NEWLINE u(0,x)=u_0(x),\quad x\geq 0,NEWLINE\]NEWLINE and the boundary value condition NEWLINE\[NEWLINE u(t,0)=u_1(1),\quad 0\leq t\leq T,NEWLINE\]NEWLINE where \(a\) is a real constant. Established are conditions of nonlocal existence and uniqueness of generalized solutions.