EXISTENCE, UNIQUENESS AND STABILITY SOLUTION OF VOLTERRA FRIEDHOLM OF INTEGRO DIFFERENTIAL EQUATIONS

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In [20], [21] and [33] the authors set up the mathematical framework to study the viscous primitive equations for the atmosphere and ocean circulation. Moreover, similar to the 3 D Navier-Stokes equations, they have shown the global existence of weak[r]

1. Introduction
The existence of a positive solution of di ff erence equations is often encountered when analysing mathematical models describing various processes. This is a motivation for an intensive study of the conditions for the existence of[r]

nonlinear, convex and nondi ff erentiable term, using auxiliary principle method in the set-
ting of reflexive Banach space.
In recent years, one step and two-step iteration algorithms (including Mann Iteration and Ishikawa iteration processes as the most important c[r]

Our paper is organized as follows: in Sect. 2 , we made some preliminary results and assumptions which play an important role in this paper. The Sect. 3 did essentially the study of existence and uniqueness of mild solution of Eq. ( 1.1 ) via[r]

under boundary conditions 1.2 . Here p, m, k , and b are given positive numbers, γ is given real number, a x is a C 1 0 , l function, and a x ≥ − c 0 > 0for all x ∈ 0 , l . It is shown that the zero solution of the problem 1.3 - 1.2 is globally asymptotically[r]

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VỀ TÍNH DUY NHẤT NGHIỆM NHỚT CỦA PHƯƠNG TRÌNH ĐẠO HÀM RIÊNG CẤP HAI LOẠI PARABOLIC ON THE UNIQUENESS OF VISCOSITY SOLUTIONS TO SECOND ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS NGUYỄ[r]

Week 3: Chemistry and First-Order Ordinary Differential Equations Jump to Solution 3 see page 42.. Question 4: The Average Speed of Gas Molecules.[r]

2. Statement of main results
We first introduce the following abbreviations: Q T = Ω × (0, T ), Σ T = ∂ Ω × (0, T ),
· p = · L p ( Ω ) , · k , p = · W k , p ( Ω ) . For simplicity, we denote · 2 by · . For every
q ∈ (1, ∞ ), we denote the dual of W 0 1, q by W −1, q w[r]

2. Statement of main results
We first introduce the following abbreviations: Q T = Ω × (0, T ), Σ T = ∂ Ω × (0, T ),
· p = · L p ( Ω ) , · k , p = · W k , p ( Ω ) . For simplicity, we denote · 2 by · . For every
q ∈ (1, ∞ ), we denote the dual of W 0 1, q by W −1, q w[r]

The real financial models such as the short term interest rates, the log-volatility in Heston model are very well modeled by a fractional Brownian motion. This fact raises a question of developing a fractional generalization of the classical processes such as Cox - Ingersoll - Ross process, Bessel p[r]

Chapter 1
Existence and uniqueness of solutions
The aims of this Chapter is to prove the existence and uniqueness of so- lutions. In Section 2.1, we give some hypothesis and a definition of weak solutions. The exis[r]

hyperbolic equation,” Journal of Di ff erential Equations, vol. 73, no. 2, pp. 197–214, 1988.
[10] J. Liu, “Singular perturbations of integrodi ff erential equations in Banach space,” Proceedings of
the American Mathematical Society, vol. 122, no. 3, pp. 791–799,[r]

We will prove the global existence and uniqueness of strong solutions in Sections 3 and 4, respectively, while Section 2 is devoted to the derivation of some a priori estimates.
We end this section by introducing some notations which will be used throughou[r]

Trong bài báo này, chúng tôi đ ã s ử d ụ ng ph ươ ng trình tích phân Volterra để gi ả i ph ươ ng trình vi phân tuy ế n tính c ấ p 1, c ấ p 2 m ộ t cách t ổ ng quát. T ừ đ ó, ch ỉ ra công th ứ c nghi ệ m t ườ ng minh cho tr ườ ng h ợ p h ệ s ố h ằ ng.
ABSTRACT

This paper studies the robust stability of implicit dynamic equations on time scales, which is a general form of differential algebraic equations and implicit difference equations. The paper discusses the reservation of exponential stability of these equations under small Lipschitz perturbations.

In this paper, we study the existence and uniqueness of fuzzy solutions for general hyperbolic partial differential equations with local conditions making use of the Banach fixed point theorem. Some examples are presented to illustrate our results.