On the porous medium equations with lower order singular nonlinear terms

1985 ◽  
Vol 45 (3-4) ◽  
pp. 425-436 ◽  
Author(s):  
G. Francsics
Keyword(s):  
Porous Medium ◽  
Lower Order ◽  
Porous Medium Equations

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.

scholarly journals Decay Estimates for Solutions of Porous Medium Equations with Advection

2019 ◽  
Vol 165 (1) ◽  
pp. 149-162
Author(s):  
Nicolau M. L. Diehl ◽  
Lucineia Fabris ◽  
Juliana S. Ziebell
Keyword(s):  
Porous Medium ◽  
Decay Estimates ◽  
Porous Medium Equations

Long-time behaviour for porous medium equations with convection

1998 ◽  
Vol 128 (2) ◽  
pp. 315-336 ◽  
Author(s):  
Ph. Laurençot ◽  
F. Simondon
Keyword(s):  
Porous Medium ◽  
Real Line ◽  
Integrable Function ◽  
Time Profile ◽  
Decay Estimates ◽  
Time Behaviour ◽  
Temporal Decay ◽  
Long Time Behaviour ◽  
Long Time ◽  
Porous Medium Equations

Long-time behaviour of solutions to porous medium equations with convection is investigated when the initial datum is a non-negative and integrable function on the real line. The long-time profile of the solutions is determined, and depends on whether the convective or the diffusive effect dominates for large times. Sharp temporal decay estimates are also provided.

scholarly journals System of porous medium equations

2021 ◽  
Vol 272 ◽  
pp. 433-472
Author(s):  
Sunghoon Kim ◽  
Ki-Ahm Lee
Keyword(s):  
Porous Medium ◽  
Porous Medium Equations

Nonnegativity preserving convergent schemes for stochastic porous-medium equations

2018 ◽  
Vol 88 (317) ◽  
pp. 1021-1059
Author(s):  
Hubertus Grillmeier ◽  
Günther Grün
Keyword(s):  
Porous Medium ◽  
Porous Medium Equations

scholarly journals A supnorm estimate for one-dimensional porous medium equations with advection

2017 ◽  
Author(s):  
Juliana Ziebell ◽  
Lucinéia Fabris ◽  
Janaina Zingano ◽  
Linéia Schütz
Keyword(s):  
Porous Medium ◽  
One Dimensional ◽  
Porous Medium Equations
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