CAUCHY PROBLEM FOR A MODEL OF A REACTIVE MIXTURE OF GASES

2021 ◽  
Vol 3 (1) ◽  
pp. 102-113
Author(s):  
Aibek Mamadalievich Toktorbaev
Keyword(s):  
Cauchy Problem ◽  
Reactive Mixture

Cauchy Problem for Equations with Fractional Differentiation Bessel Operator in the Space of Temperate Distributions

2003 ◽  
Vol 8 (1) ◽  
pp. 61-75
Author(s):  
V. Litovchenko
Keyword(s):  
Functional Analysis ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Initial Function ◽  
Well Posedness ◽  
Fractional Differentiation ◽  
Basic Tool ◽  
Conjugate Space ◽  
Analysis Technique ◽  
The Cauchy Problem

The well-posedness of the Cauchy problem, mentioned in title, is studied. The main result means that the solution of this problem is usual C∞ - function on the space argument, if the initial function is a real functional on the conjugate space to the space, containing the fundamental solution of the corresponding problem. The basic tool for the proof is the functional analysis technique.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

RANKING OF FUEL-AIR MIXTURES IN TERMS OF THEIR PROPENSITYTO DEFLAGRATION-TO-DETONATION TRANSITION

2020 ◽  
Author(s):  
S. M. FROLOV ◽  
◽  
V. I. ZVEGINTSEV ◽  
V. S. AKSENOV ◽  
I. V. BILERA ◽  
...  
Keyword(s):  
Detonation Wave ◽  
The Other ◽  
Practical Application ◽  
Deflagration To Detonation Transition ◽  
Other Hand ◽  
Pressure Gain Combustion ◽  
Reactive Mixture ◽  
Detonation Transition ◽  
The One ◽  
Energy Converting

The term "detonability" with respect to fuel-air mixtures (FAMs) implies the ability of a reactive mixture of a given composition to support the propagation of a stationary detonation wave in various thermodynamic and gasdynamic conditions. The detonability of FAMs, on the one hand, determines their explosion hazards during storage, transportation, and use in various sectors of the economy and, on the other hand, the possibility of their practical application in advanced energy-converting devices operating on detonative pressure gain combustion.

Fundamental Serrin type regularity criteria for 3D MHD fluid passing through the porous medium

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1287-1293 ◽  
Author(s):  
Zujin Zhang ◽  
Dingxing Zhong ◽  
Shujing Gao ◽  
Shulin Qiu
Keyword(s):  
Cauchy Problem ◽  
Porous Medium ◽  
Regularity Criterion ◽  
Regularity Criteria ◽  
The Cauchy Problem ◽  
Appl Math

In this paper, we consider the Cauchy problem for the 3D MHD fluid passing through the porous medium, and provide some fundamental Serrin type regularity criteria involving the velocity or its gradient, the pressure or its gradient. This extends and improves [S. Rahman, Regularity criterion for 3D MHD fluid passing through the porous medium in terms of gradient pressure, J. Comput. Appl. Math., 270 (2014), 88-99].

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