Convergence to strong nonlinear diffusion waves for solutions to p-system with damping on quadrant

AbstractIn this paper, we consider the so-called p-system with linear damping on quadrant. We show that for a certain class of given large initial data (v0(x),u0(x)), the corresponding initial–boundary value problem admits a unique global smooth solution (v(x,t),u(x,t)) and such a solution tends time-asymptotically, at the Lp (2⩽p⩽∞) optimal decay rates, to the corresponding nonlinear diffusion wave (v¯(x,t),u¯(x,t)) which satisfies (1.9) provided the corresponding prescribed initial error function (V0(x),U0(x)) lies in (H3(R+)∩L1(R+))×(H2(R+)∩L1(R+))