Convergence rates to nonlinear diffusion waves for $p$-system with nonlinear damping on quadrant
Convergence rates to nonlinear diffusion waves for $p$-system with nonlinear damping on quadrant
In this paper, we study the asymptotic behavior and the convergencerates of solutions to the so-called $p$-system with nonlineardamping on quadrant $\mathbb{R^+}\times \mathbb{R^+}=(0,\infty)\times (0,\infty)$, $v_t$-u_x=0, $u_t$+p(v)_x=-αu-g(u)with the Dirichlet boundary condition $u|_{x=0}=0$ or the Neumannboundary condition $u_x|_{x=0}=0$. The initial data $(v_0,u_0)(x)$has the constant states $(v_+,u_+)$ at $x=\infty$. In the case ofnull-Dirichlet …