scholarly journals Quenching phenomena in strongly degenerate diffusion equations with strong absorption

2003 ◽  
Vol 288 (2) ◽  
pp. 481-504 ◽  
Author(s):  
Michael Winkler
Keyword(s):  
Strong Absorption ◽  
Diffusion Equations ◽  
Degenerate Diffusion ◽  
Degenerate Diffusion Equations ◽  
Strongly Degenerate

scholarly journals Solutions to aggregation–diffusion equations with nonlinear mobility constructed via a deterministic particle approximation

2018 ◽  
Vol 28 (09) ◽  
pp. 1801-1829 ◽  
Author(s):  
Simone Fagioli ◽  
Emanuela Radici
Keyword(s):  
Large Particle ◽  
Continuity Equation ◽  
Weak Type ◽  
Closed Interval ◽  
Diffusion Equations ◽  
Degenerate Diffusion ◽  
Degenerate Diffusion Equations ◽  
Diffusion Function ◽  
Strongly Degenerate ◽  
Particle Approximation

We investigate the existence of weak type solutions for a class of aggregation–diffusion PDEs with nonlinear mobility obtained as large particle limit of a suitable nonlocal version of the follow-the-leader scheme, which is interpreted as the discrete Lagrangian approximation of the target continuity equation. We restrict the analysis to bounded, non-negative initial data with bounded variation and away from vacuum, supported in a closed interval with zero-velocity boundary conditions. The main novelties of this work concern the presence of a nonlinear mobility term and the non-strict monotonicity of the diffusion function. As a consequence, our result applies also to strongly degenerate diffusion equations. The results are complemented with some numerical simulations.

Gradient estimates for degenerate diffusion equations. I

1982 ◽  
Vol 259 (1) ◽  
pp. 53-70 ◽  
Author(s):  
Nicholas D. Alikakos ◽  
Rouben Rostamian
Keyword(s):  
Diffusion Equations ◽  
Gradient Estimates ◽  
Degenerate Diffusion ◽  
Degenerate Diffusion Equations
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