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 :