Some nonlinear degenerate diffusion equations related to population dynamics (Q791471)

This paper deals with diffusion equations of the form \[ u_ t=(u^ m)_{xx}+(\phi '(\int^{x}_{-\infty}u(\xi,t)d\xi))_ x,\quad - \infty<x<+\infty,\quad t>0 \] where \(m>1\) and \(\phi\) is smooth. Global existence, uniqueness and regularity theorems for an initial value problem \(u(x,0)=u_ 0\geq 0\), \(u_ 0\) bounded and integrable, are proved by converting this problem to an associated Cauchy problem.