Record number :

1563054

Title of article :

Cauchy problem for fast diffusion equations with a gradient term

Author/Authors :

Shang، نويسنده , , Haifeng، نويسنده ,

Issue Information :

دوهفته نامه با شماره پیاپی سال 2012

Pages :

12

From page :

133

To page :

144

Abstract :

We study the Cauchy problem for fast diffusion equation with a gradient term of the form u t − Δ u m = | D u q | σ , where 0 < m < 1 , q > 0 and 0 < σ < 2 . The existence of solutions and the optimality of the stipulated assumptions to the existence of solutions were obtained by Andreucci for the case m ≥ 1 and q σ ≥ m . Here we extend these results to the case 0 < m < 1 and all q , σ > 0 . However, as q σ > m , the optimality of the stipulated assumptions is left open.

Keywords :

Measures as initial data , Cauchy problem , Fast diffusion equation , Gradient term

Journal title :

Journal of Mathematical Analysis and Applications

Link To Document :