Global boundedness and large time behavior of solutions to a chemotaxis-consumption system with signal-dependent motility (Q2026476)

The system \(u_t=\Delta(\gamma(v)u)\), \(v_t=\Delta v-uv\) is studied in bounded domains of \({\mathbb R}^n\). If the motility function \(\gamma\) is smooth (\(C^3\)) and strictly positive, global-in-time classical solutions are shown to exist and converge to constant equilibria for the initial data \(v_0\) small in \(L^\infty\). When \(\gamma\) is merely nonnegative, suitable weak solutions exist.