scholarly journals A priori estimates of the mass of the burnt materials in rooms of buildings in the integral mathematical model of the initial stage of the fire

2021 ◽  
Vol 262 ◽  
pp. 01006
Author(s):  
Victoria Pavlidis ◽  
Yury Fedorov ◽  
Marina Chkalova ◽  
Rayslu Suleymenova
Keyword(s):  
Mathematical Model ◽  
Combustion Rate ◽  
A Priori Estimates ◽  
A Priori ◽  
Ecological Situation ◽  
Combustible Material ◽  
Special Representation ◽  
Rate Of Combustion ◽  
Priori Estimates ◽  
Initial Stage

The integral mathematical model of the initial stage of a fire in the premises of buildings focuses on the problem of estimating the mass of burnt materials assuming that the data on the rate of combustion of combustible materials are not complete. A priori estimates of the mass of burnt materials are found, which do not use data on the combustible material combustion rate. To derive these estimates, a special representation of the modulus of the increment (fall) of oxygen density in a room with a fire in the initial stage was preliminarily found. Two approaches to the derivation of a priori estimates of the mass of burnt materials have been implemented - using the upper and lower estimates of the modulus of the increment (fall) of the oxygen density. A comparison of a priori estimates obtained with different approaches is performed. Research can be useful at assessment of ecological situation and consequences of the fire.

scholarly journals The study of a mathematical model of surface reactions

2014 ◽  
Vol 55 ◽  
Author(s):  
Algirdas Ambrazevičius ◽  
Gintaras Puriuškis
Keyword(s):  
Mathematical Model ◽  
Carbon Monoxide ◽  
Nitrous Oxide ◽  
Differential Equations ◽  
Classical Solution ◽  
A Priori Estimates ◽  
Surface Reactions ◽  
A Priori ◽  
Coupled System ◽  
Priori Estimates

We prove the a priori estimates of a classical solution to a coupled system of parabolic and ordinary differential equations, the latter being determined on the boundary of the domain. This system describes the model of surface reactions between carbon monoxide and nitrous oxide.

OPTIMIZATION OF THE PROCESS OF DRUG TRANSPORT IN THE ARTERY

2019 ◽  
pp. 15-20
Author(s):  
Olena Bondar
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Drug Transport ◽  
Model Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Generalized Solutions ◽  
Parabolic Model ◽  
Priori Estimates ◽  
The Mathematical Model

The article deals with a parabolic model that describes the transport of drugs into the artery. The problem of existence and uniqueness of generalized solutions of the problem is investigated. Proof of theorems is based on a priori estimates obtained in negative norms. The problem of minimizing the quality functional based on the solutions of the mathematical model equation is solved.

The Dirichlet problem for the uniformly elliptic equation in generalized weighted Morrey spaces

2020 ◽  
Vol 57 (1) ◽  
pp. 68-90 ◽  
Author(s):  
Tahir S. Gadjiev ◽  
Vagif S. Guliyev ◽  
Konul G. Suleymanova
Keyword(s):  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Morrey Spaces ◽  
Smooth Bounded Domain ◽  
Weighted Morrey Spaces ◽  
Priori Estimates ◽  
Muckenhoupt Class ◽  
Morrey Estimates ◽  
Dirichlet Boundary Problem

Abstract In this paper, we obtain generalized weighted Sobolev-Morrey estimates with weights from the Muckenhoupt class Ap by establishing boundedness of several important operators in harmonic analysis such as Hardy-Littlewood operators and Calderon-Zygmund singular integral operators in generalized weighted Morrey spaces. As a consequence, a priori estimates for the weak solutions Dirichlet boundary problem uniformly elliptic equations of higher order in generalized weighted Sobolev-Morrey spaces in a smooth bounded domain Ω ⊂ ℝn are obtained.

Convergence of the Rosenau-Korteweg-de Vries Equation to the Korteweg-de Vries One

2020 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Lorenzo di Ruvo
Keyword(s):  
A Priori Estimates ◽  
Vries Equation ◽  
A Priori ◽  
Diffusion Parameter ◽  
Priori Estimates ◽  
De Vries ◽  
Wall Interactions

The Rosenau-Korteweg-de Vries equation describes the wave-wave and wave-wall interactions. In this paper, we prove that, as the diffusion parameter is near zero, it coincides with the Korteweg-de Vries equation. The proof relies on deriving suitable a priori estimates together with an application of the Aubin-Lions Lemma.

scholarly journals About the Use of Entropy Production for the Landau–Fermi–Dirac Equation

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
R. Alonso ◽  
V. Bagland ◽  
L. Desvillettes ◽  
B. Lods
Keyword(s):  
Dirac Equation ◽  
Classical Limit ◽  
Large Time ◽  
A Priori Estimates ◽  
Landau Equation ◽  
A Priori ◽  
Time Behaviour ◽  
Entropy Dissipation ◽  
Priori Estimates ◽  
Potential Case

AbstractIn this paper, we present new estimates for the entropy dissipation of the Landau–Fermi–Dirac equation (with hard or moderately soft potentials) in terms of a weighted relative Fisher information adapted to this equation. Such estimates are used for studying the large time behaviour of the equation, as well as for providing new a priori estimates (in the soft potential case). An important feature of such estimates is that they are uniform with respect to the quantum parameter. Consequently, the same estimations are recovered for the classical limit, that is the Landau equation.

scholarly journals A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said Mesloub ◽  
Hassan Eltayeb Gadain
Keyword(s):  
Differential Equations ◽  
Evolution Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
A Priori Bounds ◽  
Fractional Evolution Equation ◽  
Priori Estimates ◽  
Initial Boundary Value

Abstract A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

scholarly journals Blow-up criterion for the density dependent inviscid Boussinesq equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Li Li ◽  
Yanping Zhou
Keyword(s):  
Velocity Field ◽  
Energy Method ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Boussinesq Equations ◽  
Smooth Solutions ◽  
Density Dependent ◽  
Priori Estimates ◽  
Blow Up Criterion

Abstract In this work, we consider the density-dependent incompressible inviscid Boussinesq equations in $\mathbb{R}^{N}\ (N\geq 2)$ R N ( N ≥ 2 ) . By using the basic energy method, we first give the a priori estimates of smooth solutions and then get a blow-up criterion. This shows that the maximum norm of the gradient velocity field controls the breakdown of smooth solutions of the density-dependent inviscid Boussinesq equations. Our result extends the known blow-up criteria.

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