Results 101 to 110 of about 610,482 (163)

Preventing blow up by convective terms in dissipative PDEs

, 2015
We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type equations, convective Cahn-Hilliard equation, generalized Kuramoto ...
Bilgen, Bilgesu, Kalantarov, Varga, Zelik, Sergey   +2 more
core  

A special integral and a Gronwall inequality [PDF]

Transactions of the American Mathematical Society, 1976
This paper considers a special integral ( I ) ∫ a b ( f d g + H ) (I)\smallint _a^b(fdg + H) which is a subdivision-refinement-type limit of the approximating sum \[ ∑ 1 n
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Strong solutions to the 3D primitive equations with only horizontal dissipation: near $H^1$ initial data

, 2016
In this paper, we consider the initial-boundary value problem of the three-dimensional primitive equations for oceanic and atmospheric dynamics with only horizontal viscosity and horizontal diffusivity.
Cao, Chongsheng, Li, Jinkai, Titi, Edriss S.   +2 more
core  

Exponentially stable solution of mathematical model of agents dynamics on time scales

Advances in Difference Equations, 2019
This work is an attempt at studying leader-following model on the arbitrary time scale. The step size is treated as a function of time. Our purpose is establishing conditions ensuring a leader-following consensus for any time scale basing on the Grönwall
Ewa Schmeidel, Urszula Ostaszewska, Małgorzata Zdanowicz   +2 more
doaj   +1 more source

On Gronwall's Inequality [PDF]

Proceedings of the American Mathematical Society, 1967
Chu, C. S., Metcalf, F. T.
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Note on fractional difference Gronwall inequalities

Electronic Journal of Qualitative Theory of Differential Equations, 2014
Summary: This note is a reaction on a bunch of fractional inequalities that appeared in the last few years, and that are all based on what claims to be a fractional discrete Gronwall inequality. However, we show by a counterexample that this inequality is not correct.
Feckan, Michal, Pospíšil, Michal
openaire   +3 more sources

The Generalized Gronwall Inequality and Its Application to Periodic Solutions of Integrodifferential Impulsive Periodic System on Banach Space

, 2008
This paper deals with a class of integrodifferential impulsive periodic systems on Banach space. Using impulsive periodic evolution operator given by us, the -periodic PC-mild solution is introduced and suitable Poincaré operator is constructed.
Jin Rong Wang, X. Xiang, W. Wei, Qian Chen   +3 more
semanticscholar   +1 more source

An Asymptotic Behavior Property of High-Order Nonlinear Dynamic Equations on Time Scales

Axioms
In this work, by using one dynamic Gronwall–Bihari-type integral inequality on time scales, an interesting asymptotic behavior property of high-order nonlinear dynamic equations on time scales was obtained, which also generalized two classical results ...
Yuan Yuan, Qinghua Ma
doaj   +1 more source

Finite-Time Stability of Fractional-Order BAM Neural Networks with Distributed Delay

Abstract and Applied Analysis, 2014
Based on the theory of fractional calculus, the generalized Gronwall inequality and estimates of mittag-Leffer functions, the finite-time stability of Caputo fractional-order BAM neural networks with distributed delay is investigated in this paper.
Yuping Cao, Chuanzhi Bai
doaj   +1 more source

The Gronwall inequality

We prove the following version generalization of the Gronwall inequality: Let $\mathbf X$ be a Banach space and $U\subset \mathbf X$ an open convex set in $\mathbf X$. Let $f,g\colon [a,b]\times U\to \mathbf X$ be continuous functions and let $y,z\colon [a,b]\to U$ satisfy the initial value problems \begin{align*} y'(t)&=f(t,y(t)),\quad y(a)=y_0,\\
openaire   +2 more sources