Nonlinear PDE Phenomena

1997 ◽  
pp. 291-316
Author(s):  
Richard H. Enns ◽  
George McGuire
Keyword(s):  
Nonlinear Pde

On a doubly nonlinear PDE with stochastic perturbation

2018 ◽  
Vol 7 (2) ◽  
pp. 297-330 ◽  
Author(s):  
Niklas Sapountzoglou ◽  
Petra Wittbold ◽  
Aleksandra Zimmermann
Keyword(s):  
Stochastic Perturbation ◽  
Nonlinear Pde ◽  
Doubly Nonlinear

scholarly journals Pollution Transfer as Optimal Mass Transport Problem

2016 ◽  
Vol 8 (6) ◽  
pp. 58
Author(s):  
L. Ndiaye ◽  
Mb. Ndiaye ◽  
A. Sy ◽  
D. Seck
Keyword(s):  
Porous Media ◽  
Optimal Transport ◽  
Existence Of Solution ◽  
Nonlinear Pde ◽  
Mathematical Framework ◽  
Sufficient Condition ◽  
Mass Transportation ◽  
Optimal Mass Transport ◽  
Transportation Theory ◽  
Optimal Transport Map

In this paper, we use mass transportation theory to study pollution  transfer in  porous media.  We show   the existence of a $L^2-$regular vector field defined by a $W^{1, 1}-$ optimal transport map. A sufficient condition for solvability of our model, is given by   a (non homogeneous) transport equation with  a  source defined by a measure. The mathematical framework used, allows us to  show in some specifical cases, existence of solution for  a nonlinear PDE deriving from the modelling. And we end by numerical simulations.

scholarly journals On the macroscopic limit of Brownian particles with local interaction

2020 ◽  
Vol 20 (06) ◽  
pp. 2040007
Author(s):  
Franco Flandoli ◽  
Marta Leocata ◽  
Cristiano Ricci
Keyword(s):  
Explicit Form ◽  
Diffusion Processes ◽  
Particle System ◽  
Local Interaction ◽  
Nonlinear Pde ◽  
Rigorous Results ◽  
Precise Form ◽  
Interacting Particle ◽  
Brownian Particles ◽  
Main Ideas

An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. This paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical informations on the precise form of the nonlinearity which are new with respect to the literature and coherent with the few known informations.

scholarly journals Designing Optical Fibers: Fitting the Derivatives of a Nonlinear Pde-Eigenvalue Problem

2012 ◽  
Vol 02 (04) ◽  
pp. 321-330 ◽  
Author(s):  
Linda Kaufman ◽  
Seok-Min Bang ◽  
Brian Heacook ◽  
William Landon ◽  
Daniel Savacool ◽  
...  
Keyword(s):  
Eigenvalue Problem ◽  
Optical Fibers ◽  
Nonlinear Pde ◽  
Derivatives Of
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