scholarly journals Global existence, uniqueness, and continuous dependence for a semilinear initial value problem

2003 ◽  
Vol 280 (2) ◽  
pp. 413-423 ◽  
Author(s):  
Francisco Periago
Keyword(s):  
Global Existence ◽  
Initial Value Problem ◽  
Continuous Dependence ◽  
Initial Value

scholarly journals Remarks on the critical nonlinear high-order heat equation

2019 ◽  
Vol 26 (1/2) ◽  
pp. 127-152
Author(s):  
Tarek Saanouni
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
High Order ◽  
Well Posedness ◽  
Potential Well ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Nonlinear High Order

The initial value problem for a semi-linear high-order heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.

scholarly journals Global existence for abstract nonlinear Volterra–Fredholm functional integrodifferential equation

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
M. B. Dhakne ◽  
Kishor D. Kucche
Keyword(s):  
Global Existence ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Initial Value Problem ◽  
Existence Of Solutions ◽  
A Priori ◽  
A Priori Bounds ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Fredholm Functional

AbstractIn the present paper, we investigate the global existence of solutions to initial value problem for nonlinear mixed Volterra–Fredholm functional integrodifferential equations in Banach spaces. The technique used in our analysis is based on an application of the topological transversality theorem known as Leray–Schauder alternative and rely on a priori bounds of solution.

scholarly journals Continuous dependence and convergence for a Kelvin–Voigt fluid of order one

2021 ◽  
Author(s):  
Brian Straughan
Keyword(s):  
Initial Value Problem ◽  
Continuous Dependence ◽  
Initial Value ◽  
Voigt Fluid

AbstractIt is shown that the solution to the boundary - initial value problem for a Kelvin–Voigt fluid of order one depends continuously upon the Kelvin–Voigt parameters, the viscosity, and the viscoelastic coefficients. Convergence of a solution is also shown.

HOPF SOLUTIONS TO A FLUID-ELASTIC INTERACTION MODEL

2008 ◽  
Vol 18 (02) ◽  
pp. 215-269 ◽  
Author(s):  
M. GUIDORZI ◽  
M. PADULA ◽  
P. I. PLOTNIKOV
Keyword(s):  
Global Existence ◽  
Existence Theorem ◽  
Initial Value Problem ◽  
Interaction Model ◽  
Elastic Interaction ◽  
Initial Condition ◽  
Two Dimensional ◽  
Initial Value ◽  
Global Existence Theorem ◽  
Model Equations

In this paper, we give a global existence theorem of weak solutions to model equations governing interaction fluid structure in a two-dimensional layer, cf. Refs. 8 and 14. To our knowledge this is the first existence theorem of global in time solutions for such model. The interest of our result is double because, first, we change the original initial value problem by deleting one initial condition, second, we construct a solution through the classical Galerkin method for which several computing codes have been constructed.

scholarly journals Integral inequalities of Gronwall type for piecewise continuous functions

1997 ◽  
Vol 10 (1) ◽  
pp. 89-94 ◽  
Author(s):  
Drumi D. Bainov ◽  
Snezhana G. Hristova
Keyword(s):  
Differential Equations ◽  
Integral Inequality ◽  
Initial Value Problem ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Continuous Functions ◽  
Integral Inequalities ◽  
Initial Value ◽  
Volterra Type ◽  
Piecewise Continuous

In this paper we generalize the integral inequality of Gronwall and study the continuous dependence of the solution of the initial value problem for nonlinear impulsive integro-differential equations of Volterra type on the initial conditions.

scholarly journals Global existence of small displacement solutions for Hookean incompressible viscoelasticity in 3D

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Boyan Jonov ◽  
Paul Kessenich ◽  
Thomas C. Sideris
Keyword(s):  
Global Existence ◽  
Initial Value Problem ◽  
Strong Solutions ◽  
Small Displacement ◽  
Initial Value ◽  
Global Strong Solutions ◽  
Three Space

<p style='text-indent:20px;'>The initial value problem for incompressible Hookean viscoelastic motion in three space dimensions has global strong solutions with small displacements.</p>

An Estimate of the Bound of the Lyapunov Exponents for Caputo-Hadamard Fractional Differential System

2021 ◽  
Author(s):  
Changpin Li ◽  
Chuntao Yin
Keyword(s):  
Lyapunov Exponents ◽  
Differential System ◽  
Initial Value Problem ◽  
Continuous Dependence ◽  
Initial Value ◽  
Numerical Examples ◽  
Fractional Differential System ◽  
Grönwall Inequality ◽  
Fractional Differential ◽  
Theoretical Results

Abstract This paper is devoted to estimating the bound of the Lyapunov exponents for the Caputo-Hadamard fractional differential system. First, using the Gronwall inequality, we analyze the continuous dependence of the solution to the Caputo-Hadamard fractional initial value problem. Then, we define the Lyapunov exponents for the Caputo-Hadamard fractional differential system and estimate their bounds. Besides, numerical examples are displayed which support the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document