scholarly journals Extinction and decay estimates of solutions for a porous medium equation with nonlocal source and strong absorption

2013 ◽  
Vol 2013 (1) ◽  
pp. 24 ◽  
Author(s):  
Xianghui Xu ◽  
Zhong Fang ◽  
Su-Cheol Yi
Keyword(s):  
Porous Medium ◽  
Porous Medium Equation ◽  
Strong Absorption ◽  
Decay Estimates ◽  
Nonlocal Source ◽  
Estimates Of Solutions ◽  
Medium Equation

Pointwise estimates of solutions to the weighted porous medium equation and the fast diffusion one via weighted Riesz potentials

2020 ◽  
Vol 17 (1) ◽  
pp. 116-143
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Riesz Potential ◽  
Porous Medium Equation ◽  
Fast Diffusion ◽  
Pointwise Estimates ◽  
Riesz Potentials ◽  
Local Boundedness ◽  
Estimates Of Solutions ◽  
Medium Equation ◽  
The Right

For the weighted parabolic equation $$ \ v\left(x \right)u_{t} - {div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1}, $$ we prove the local boundedness of weak solutions in terms of the ${\;}$ weighted Riesz potential on the right-hand side of the equation.

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