The mixed initial-boundary value problem for diagonalizable quasilinear hyperbolic systems in the first quadrant Original Research Article

In this paper, we investigate the mixed initial-boundary value problem for diagonalizable quasilinear hyperbolic systems with nonlinear boundary conditions on a half-unbounded domain View the MathML source{(t,x)|t≥0,x≥0}. Under the assumptions that system is strictly hyperbolic and linearly degenerate, we obtain the global existence and uniqueness of C1C1 solutions with the bounded L1∩L∞L1∩L∞ norm of the initial data as well as their derivatives and appropriate boundary condition. Based on the existence results of global classical solutions, we also prove that when tt tends to infinity, the solutions approach a combination of C1C1 travelling wave solutions. Under the appropriate assumptions of initial and boundary data, the results can be applied to the equation of time-like extremal surface in Minkowski space R1+(1+n)R1+(1+n).