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.

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 Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections

2020 ◽  
Author(s):  
Hanwu Li ◽  
Yongsheng Song
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Backward Stochastic Differential Equations ◽  
Penalization Method ◽  
Priori Estimates ◽  
Uniqueness And Existence

Abstract In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the solution lies between two prescribed processes. A new kind of approximate Skorohod condition is proposed to derive the uniqueness and existence of the solutions. The uniqueness can be proved by a priori estimates and the existence is obtained via a penalization method.

scholarly journals Analytical solution of a class of nonlinear differential equations of the third order in the complex area

2021 ◽  
pp. 75-84
Author(s):  
Виктор Николаевич Орлов ◽  
Людмила Витальевна Мустафина
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
A Priori Estimate ◽  
Third Order ◽  
The Third ◽  
Change Of Variables ◽  
Priori Estimates

В работе приводится доказательство теоремы существования и единственности аналитического решения класса нелинейных дифференциальных уравнений третьего порядка, правая часть которого представлена полиномом шестой степени, в комплексной области. Расширен класс рассматриваемых уравнений за счет новой замены переменных. Получена априорная оценка аналитического приближенного решения. Представлен вариант численного эксперимента оптимизации априорных оценок с помощью апостериорных. The article presents a proof of the theorem of the existence and uniqueness of the analytical solution of the class of nonlinear differential equations of the third order, with a polynomial right-hand side of the sixth degree, in the complex domain. The class of the considered equations has been extended by means of a new change of variables. An a priori estimate of the analytical approximate solution is obtained. A variant of the numerical experiment of optimizing a priori estimates using a posteriori estimates is presented.

scholarly journals Periodic solutions for second order differential equations with indefinite singularities

2019 ◽  
Vol 9 (1) ◽  
pp. 994-1007 ◽  
Author(s):  
Shiping Lu ◽  
Xingchen Yu
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
A Priori Estimates ◽  
A Priori ◽  
Second Order ◽  
Continuation Theorem ◽  
Second Order Differential Equations ◽  
Priori Estimates ◽  
Negative Constant

Abstract In this paper, the problem of periodic solutions is studied for second order differential equations with indefinite singularities $$\begin{array}{} \displaystyle x''(t)+ f(x(t))x'(t)+\varphi(t)x^m(t)-\frac{\alpha(t)}{x^\mu(t)}+\frac{\beta(t)}{x^y (t)}=0, \end{array}$$ where f ∈ C((0, +∞), ℝ) may have a singularity at the origin, the signs of φ and α are allowed to change, m is a non-negative constant, μ and y are positive constants. The approach is based on a continuation theorem of Manásevich and Mawhin with techniques of a priori estimates.

Solvability of a mathematical model of dissociative adsorption and associative desorption type

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Algirdas Ambrazevičius ◽  
Alicija Eismontaitė
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Classical Solution ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Diatomic Molecules ◽  
Coupled System ◽  
Dissociative Adsorption ◽  
Existence And Uniqueness Theorem

AbstractA mathematical model of dissociative adsorption and associative desorption for diatomic molecules is generalized. The model is described by a coupled system of parabolic and ordinary differential equations. The existence and uniqueness theorem of the classical solution is proved.

scholarly journals Regularizing Model for the 2D MHD Equations with Zero Viscosity

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Ensil Kang ◽  
Jihoon Lee
Keyword(s):  
Classical Solution ◽  
A Priori Estimates ◽  
A Priori ◽  
Mhd Equations ◽  
Two Dimensional ◽  
System A ◽  
Priori Estimates ◽  
Zero Viscosity ◽  
Time Existence ◽  
Hydrodynamics Equations

We consider the regularity of two dimensional incompressible magneto-hydrodynamics equations with zero viscosity. We provide an approximating system to the equations and prove global-in-time existence of classical solution to this approximating system. By using approximating system, a priori estimates for the equations can be justified.

Numerical analysis of nonlinear model of excited carrier decay

2013 ◽  
Vol 11 (6) ◽  
Author(s):  
Natalija Tumanova ◽  
Raimondas Čiegis ◽  
Mečislavas Meilūnas
Keyword(s):  
Differential Equations ◽  
A Priori Estimates ◽  
Nonlinear Differential Equations ◽  
A Priori ◽  
Euler Method ◽  
Genetic Optimization ◽  
Identifiability Analysis ◽  
Priori Estimates ◽  
Backward Euler ◽  
Excited Carrier

AbstractThis paper presents a mathematical model for photo-excited carrier decay in a semiconductor. Due to the carrier trapping states and recombination centers in the bandgap, the carrier decay process is defined by the system of nonlinear differential equations. The system of nonlinear ordinary differential equations is approximated by linearized backward Euler scheme. Some a priori estimates of the discrete solution are obtained and the convergence of the linearized backward Euler method is proved. The identifiability analysis of the parameters of deep centers is performed and the fitting of the model to experimental data is done by using the genetic optimization algorithm. Results of numerical experiments are presented.

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