Nonlocal well-posedness of mixed problem in half-region for the Korteweg-de~Vries equation (Q2719468)

This paper deals with the Korteweg-de~Vries (KdV) equation NEWLINE\[NEWLINE u_t+u_{xxx}+au_x+uu_x = f(t,x),NEWLINE\]NEWLINE where \(a\) is some real constant, which is considered in the half-region \( \Pi_T^+ = (0,T)\times \mathbb{R}_+\), with the boundary conditions NEWLINE\[NEWLINE \begin{aligned} &u(0,x) = u_0(x),\quad x\geq 0,\\ &u(t,0) = u_1(t),\quad 0\leq t\leq T.\end{aligned} NEWLINE\]NEWLINE The author establishes the conditions of nonlocal solvability, uniqueness and continuous dependence of solutions to the above-mentioned problem.