Existence and nonuniqueness of segregated solutions to a class of cross-diffusion systems

Gonzalo Galiano, Sergey Shmarev, Julián Velasco

We study the the Dirichlet problem for the cross-diffusion system \[ \partial_tu_i=\operatorname{div}\left(a_iu_i\nabla (u_1+u_2)\right)+f_i(u_1,u_2),\quad i=1,2,\quad a_i=const>0,…