Existence of traveling waves in Fermi–Pasta–Ulam–type systems on a 2D–lattice

2021 ◽  
Vol 252 (4) ◽  
pp. 453-462
Author(s):  
Sergiy Mykolayovych Bak ◽  
Galyna Mykolayivna Kovtonyuk
Keyword(s):  
2018 ◽  
Vol 28 (11) ◽  
pp. 2103-2129 ◽  
Author(s):  
Margarita Arias ◽  
Juan Campos ◽  
Juan Soler

This paper deals with the analysis of qualitative properties involved in the dynamics of Keller–Segel type systems in which the diffusion mechanisms of the cells are driven by porous-media flux-saturated phenomena. We study the regularization inside the support of a solution with jump discontinuity at the boundary of the support. We analyze the behavior of the size of the support and blow-up of the solution, and the possible convergence in finite time toward a Dirac mass in terms of the three constants of the system: the mass, the flux-saturated characteristic speed, and the chemoattractant sensitivity constant. These constants of motion also characterize the dynamics of regular and singular traveling waves.


2020 ◽  
Vol 17 (3) ◽  
pp. 301-312
Author(s):  
Sergiy Bak ◽  
Galyna Kovtonyuk

The article deals with the Fermi-Pasta-Ulam-type systems that describe infinite systems of particles on a 2D lattice. The main result concerns the existence of the solutions corresponding to traveling waves with periodic and vanishing profiles. By means of the critical point theory, the sufficient conditions for the existence of such solutions are obtained.


1997 ◽  
Vol 35 (7) ◽  
pp. 187-195 ◽  
Author(s):  
Binle Lin ◽  
K. Futono ◽  
A. Yokoi ◽  
M. Hosomi ◽  
A. Murakami

Establishing economic treatment technology for safe disposal of photo-processing waste (PW) has most recently become an urgent environmental concern. This paper describes a new biological treatment process for PW using sulfur-oxidizing bacteria (SOB) in conjunction with activated carbon (AC). Batch-type acclimation and adsorption experiments using SOB/PAC, SOB/PNAC, and SOB reactor type systems demonstrated that AC effectively adsorbs the toxic/refractory compounds which inhibit thiosulfate oxidization of SOB in PW. Thus, to further clarify the effect of AC, we performed a long-term (≈ 160 d) continuous-treatment experiment on 4- to 8-times dilution of PW using a SOB/GAC system which simulated a typical wastewater treatment system based on an aerobic activated sludge process that primarily uses acclimated SOB. The thiosulfate load and hydraulic retention time (HRT) were fixed during treatment such that they ranged from 0.8-3.7 kg S2O32-/l/d and 7.7-1.9 d, respectively. As expected, continuous treatment led to breakthrough of the adsorption effect of GAC. Renewing the GAC and continuing treatment for about 10 d demonstrated good treatment effectiveness.


Author(s):  
V. M. Es'kov ◽  
◽  
V. V. Grigorenko ◽  
N. B. Nazina ◽  
◽  
...  
Keyword(s):  

1996 ◽  
Vol 100 (40) ◽  
pp. 16209-16212 ◽  
Author(s):  
John A. Pojman ◽  
Andrea Komlósi ◽  
Istvan P. Nagy

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