The Hölder property in some degenerate parabolic problems (Q1821263)

The Hölder continuity of the degenerate parabolic equation \[ uu_{xx}+u^ 2_ x +h(x,t,u)u=u_ t \] with nonnegative initial data \(u_ 0(x)\) is demonstrated. In particular, it is shown that \(| u|_{\alpha}\leq K\), where K is independent of the modulus of continuity of h. A similar result is proved for the porous medium equation \(u_ t=(u^ m)_{xx}+h(x,t,u)u\).