Harnack inequalities for a class of heat flows with nonlinear reaction terms

Author(s):  
Abimbola Abolarinwa ◽  
Julius Osato Ehigie ◽  
Ali H. Alkhaldi
2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Michel Ledoux

Abstract In a recent work, E. Cinti and F. Otto established some new interpolation inequalities in the study of pattern formation, bounding the Lr(μ)-norm of a probability density with respect to the reference measure μ by its Sobolev norm and the Kantorovich-Wasserstein distance to μ. This article emphasizes this family of interpolation inequalities, called Sobolev-Kantorovich inequalities, which may be established in the rather large setting of non-negatively curved (weighted) Riemannian manifolds by means of heat flows and Harnack inequalities.


Author(s):  
S. V. Korobkov ◽  
A. I. Gnyrya ◽  
V. I. Terekhov

The paper considers the dynamic and thermal interference effects on two neighbouring building models in the form of square prisms arranged at a short distance from each other. It is shown how relative positions of the models affect the specific phenomena caused by the airflow interactions.The aim of this paper is to experimentally study the dynamic and thermal interference of a tandem of two building models in the form of square prisms depending on their relative position.The phenomenon of wind loads on buildings and structures has always attracted great interest among engineers and researchers. With the accumulation of knowledge and technical capabilities, the potential for likely ways to study wind flows and their impact on different objects increased. In recent years, the world science has accumulated an extensive knowledge base on wind impacts on objects of various shapes, such as prisms, pyramids, cylinders, etc. Studies are carried out for their mutual impact of several objects on changes in both the wind load and heat exchange. Their mutual effect on the air motion and turbulence is considered.There are two main areas in the field of the wind impact. The first impact is the force load on building, the second is the wind as a source of convective heat exchange. The object of this study is the interference parameters allowing to assess the influence on the field of pressure and heat recoil of disturbances evoked in front of the barriers.At the first stage, physical models help to study the pressure field on different facets and ratios of the local and medium heat exchange under the forced convection conditions. The next step is to jointly consider the wind (dynamic) load and heat flows, attempting to detect the total contribution to changes depending on the reciprocal model arrangement. All experiments are performed in the aerodynamic tube, at the TSUAB department. It is shown that the dynamic and thermal interference ratios vary greatly in two building models. At the same time, the thermal interference is very conservative compared to the dynamic. Using the interference parameters, it is easy to analyze the extreme pressure and the heat flow on the model surface depending on a large number of factors, including their arrangement.


2000 ◽  
Vol 65 (9) ◽  
pp. 1394-1402 ◽  
Author(s):  
Ľubica Adamčíková ◽  
Mária Hupková ◽  
Peter Ševčík

Spatial patterns in methylene blue-catalyzed oxidation of fructose at alkaline pH were found in aqueous solution and in gel systems. In a thin liquid layer (thickness >2.4 mm) a mixture of spots and stripes was formed by interaction of a nonlinear reaction and the Rayleigh or Maragoni instabilities. The pattern formation was affected by initial reactant concentrations and by the thickness of the reaction mixture layer. Long-lasting structures were formed in gel systems (polyacrylamide, agar, gelatin). These patterns also arise primarily from hydrodynamic processes.


2014 ◽  
Vol 37 (17) ◽  
pp. 2389-2402
Author(s):  
Xiuhong Wu ◽  
Bingchang Lin ◽  
Yanling Quan ◽  
PeiXun Zhu ◽  
Hong Gao ◽  
...  

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