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.

On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

2021 ◽  
Vol 18 (1) ◽  
pp. 104-139
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Riesz Potential ◽  
Fast Diffusion ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Lower Order Terms

For the 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 continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

Harnack estimates for a kind of porous medium equation

2021 ◽  
Vol 115 ◽  
pp. 106978
Author(s):  
Feida Jiang ◽  
Xinyi Shen ◽  
Hui Wu
Keyword(s):  
Porous Medium ◽  
Porous Medium Equation ◽  
Medium Equation ◽  
Harnack Estimates
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