Asymptotic profiles for convection-diffusion equations with variable diffusion (Q5946005)

The authors investigate the large time behavior of solutions of a nonlinear convection-diffusion equation with variable diffusionNEWLINENEWLINE\[NEWLINEu_t-\text{div}(a(x)\nabla u)=d\cdot\nabla(| u|^{q-1}u), \;d\in\mathbb R^N, \text{in} (0,\infty)\times\mathbb R^N,NEWLINE\]NEWLINE with integrable data \(u_0(x)\). They show the influence of the nonlinear term and the variable diffusion in the large time behavior by obtaining the second term in the asymptotic expansion of solutions.