Convergence to steady states in a viscous Hamilton–Jacobi equation with degenerate diffusion

This paper deals with weak solutions of the one-dimensional viscous Hamilton–Jacobi equationut=(|ux|p−2ux)x+|ux|qin (−R,R)×(0,∞) with homogeneous Dirichlet boundary conditions, where R>0R>0, p>2p>2 and 1