scholarly journals Nonnegative solutions of the initial-Dirichlet problem for generalized porous medium equations in cylinders

1988 ◽  
Vol 1 (2) ◽  
pp. 401-401 ◽  
Author(s):  
Bj{örn E. J. Dahlberg ◽  
Carlos E. Kenig
Keyword(s):  
Porous Medium ◽  
Dirichlet Problem ◽  
Nonnegative Solutions ◽  
Porous Medium Equations

scholarly journals Measure Data Problems for a Class of Elliptic Equations with Mixed Absorption-Reaction

2021 ◽  
Vol 21 (2) ◽  
pp. 261-280
Author(s):  
Marie-Françoise Bidaut-Véron ◽  
Marta Garcia-Huidobro ◽  
Laurent Véron
Keyword(s):  
Dirichlet Problem ◽  
Compact Subset ◽  
Elliptic Equations ◽  
Radon Measure ◽  
Measure Data ◽  
Nonnegative Solutions

Abstract In the present paper, we study the existence of nonnegative solutions to the Dirichlet problem ℒ p , q M ⁢ u := - Δ ⁢ u + u p - M ⁢ | ∇ ⁡ u | q = μ {{\mathcal{L}}^{{M}}_{p,q}u:=-\Delta u+u^{p}-M|\nabla u|^{q}=\mu} in a domain Ω ⊂ ℝ N {\Omega\subset\mathbb{R}^{N}} where μ is a nonnegative Radon measure, when p > 1 {p>1} , q > 1 {q>1} and M ≥ 0 {M\geq 0} . We also give conditions under which nonnegative solutions of ℒ p , q M ⁢ u = 0 {{\mathcal{L}}^{{M}}_{p,q}u=0} in Ω ∖ K {\Omega\setminus K} , where K is a compact subset of Ω, can be extended as a solution of the same equation in Ω.

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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