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 On an abstract nonlinear second order integrodifferential equation

2007 ◽  
Vol 5 (2) ◽  
pp. 167-174 ◽  
Author(s):  
M. B. Dhakne ◽  
G. B. Lamb
Keyword(s):  
Banach Space ◽  
Global Existence ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
A Priori ◽  
Second Order ◽  
A Priori Bounds ◽  
Global Existence Of Solutions

The aim of the present paper is to study the global existence of solutions of nonlinear second order integrodifferential equation in Banach space. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.

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 of solutions for a multi-phase flow: A drop in a gas-tube

2016 ◽  
Vol 13 (02) ◽  
pp. 381-415
Author(s):  
Debora Amadori ◽  
Paolo Baiti ◽  
Andrea Corli ◽  
Edda Dal Santo
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Inviscid Fluid ◽  
Phase Flow ◽  
Lagrangian Coordinates ◽  
Large Initial Data ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
Multi Phase Flow ◽  
Multi Phase

In this paper we study the flow of an inviscid fluid composed by three different phases. The model is a simple hyperbolic system of three conservation laws, in Lagrangian coordinates, where the phase interfaces are stationary. Our main result concerns the global existence of weak entropic solutions to the initial-value problem for large initial data.

A SOBOLEV SPACE APPROACH TO BOUNDARY VALUE PROBLEMS ON THE HALF-LINE

2005 ◽  
Vol 07 (01) ◽  
pp. 1-36 ◽  
Author(s):  
PATRICK J. RABIER ◽  
CHARLES A. STUART
Keyword(s):  
Boundary Condition ◽  
Functional Equation ◽  
Existence Of Solutions ◽  
A Priori ◽  
Degree Theory ◽  
A Priori Bounds ◽  
Initial Value ◽  
Second Order Equations ◽  
Ode Systems ◽  
Space Approach

This paper addresses the existence of solutions u ∈ H1(ℝ+;ℝN) of ODE systems [Formula: see text], with boundary condition u1(0) = ξ, where u1is a (vector) component of u. Under general conditions, the problem corresponds to a functional equation involving a Fredholm operator with calculable index, which is proper on the closed bounded subsets of H1(ℝ+;ℝN). When the index is 0 and the solutions are bounded a priori, the existence follows from an available degree theory for such operators. Specific conditions are given that guarantee the existence of a priori bounds and second order equations with Dirichlet, Neumann or initial value conditions are discussed as applications.

Generalized Invariant Sets for the Boltzmann Equation

1997 ◽  
Vol 07 (04) ◽  
pp. 457-476 ◽  
Author(s):  
T. Goudon
Keyword(s):  
Boltzmann Equation ◽  
Initial Data ◽  
Global Existence ◽  
Existence Of Solutions ◽  
Invariant Set ◽  
Invariant Sets ◽  
Soft Or ◽  
Initial Value ◽  
Global Existence Of Solutions ◽  
The Boltzmann Equation

We are interested in the initial value problem for the Boltzmann equation, when the initial data u0 belongs to a set B0 = {δ0m1 (0,x,v) ≤ u0(x,v) ≤ C0m2 (0,x,v)} where m1, m2 are traveling Maxwellians. We consider soft or Maxwell's interactions with cutoff (7/3 < s ≤ 5) and C0 smaller than a bound depending on the coefficients of m2. We obtain global existence of solutions remaining in a "generalized invariant set" Bt ⊂ B∞, characterized by these particular states.

Global and non Global Solutions for Some Fractional Heat Equations With Pure Power Nonlinearity

2017 ◽  
Vol 69 (4) ◽  
pp. 854-872
Author(s):  
Tarek Saanouni
Keyword(s):  
Global Existence ◽  
Heat Equation ◽  
Existence Of Solutions ◽  
Global Solutions ◽  
Heat Equations ◽  
Well Posedness ◽  
Potential Well ◽  
Initial Value ◽  
Fractional Heat Equation ◽  
Global Existence Of Solutions

AbstractThe initial value problem for a semi-linear fractional 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.

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