Unique continuation for fast diffusion (Q1411745)

This paper deals with the non-characteristic Cauchy problem for the equation \[ |u|^{\alpha}u_t=\triangle u+\gamma|u|^{-\beta}u,\tag{1} \] whose lower order term contains the sublinear case. Here it is supposed that \(\frac{1}{2}<\alpha <1\), \(\alpha+\beta<1\) and \(\beta\gamma\geq 0\), and the author proves two theorems concerning the unique continuation property for the solutions of (1). Among others, the results extend analogous recent results of the author concerning the case \(\alpha\geq 1\).