The Role of an Integral Inequality in the Study of Certain Differential Equations
نویسنده
چکیده
In this paper we present an integral inequality and show how it can be used to study certain differential equations. Namely, we will see how to establish (global) existence results and determine the decay rates of solutions to abstract semilinear problems, reaction diffusion systems with time dependent coefficients and fractional differential problems. A nonlinear singular version of the Gronwall inequality is also presented.
منابع مشابه
Solution to time fractional generalized KdV of order 2q+1 and system of space fractional PDEs
Abstract. In this work, it has been shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve time fractional generalized KdV of order 2q+1 and certain fractional PDEs. It is shown that exponential operators are an effective method for solving certain fractional linear equations with non-constant coefficients. It may be concluded that the com...
متن کاملConstruction of measures of noncompactness of $C^k(Omega)$ and $C^k_0$ and their application to functional integral-differential equations
In this paper, first, we investigate the construction of compact sets of $ C^k$ and $ C_0^k$ by proving ``$C^k, C_0^k-version$" of Arzel`{a}-Ascoli theorem, and then introduce new measures of noncompactness on these spaces. Finally, as an application, we study the existence of entire solutions for a class of the functional integral-differential equations by using Darbo's fixe...
متن کاملA new block by block method for solving two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds
In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the ...
متن کاملCoupled Integral Equations Approach in the Solution of Luikov Equations with Microwave Effect
The objective of this study is to present a mathematical modeling and solution approach for the drying process of spheroidal solids with the application of microwave in capillary porous media based on the Luikov equations, composed of a system of linear and coupled partial differential equations arising from the energy, mass and pressure balances inside the solid matrix. Additionally, the power...
متن کاملA More Generalized Gronwall-like Integral Inequality with Applications
This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations. 1. Introduction. It is well known that integral inequalities play a very crucial role in the stud...
متن کامل