Negative power nonlinear integral equations on bounded domains

Partial Differential Equations on Bounded Domains

SPLINE COLLOCATION FOR NONLINEAR FREDHOLM INTEGRAL EQUATIONS

The collocation method based on cubic B-spline, is developed to approximate the solution of second kind nonlinear Fredholm integral equations. First of all, we collocate the solution by B-spline collocation method then the Newton-Cotes formula use to approximate the integrand. Convergence analysis has been investigated and proved that the quadrature rule is third order convergent. The presented...

Fractional Nonlinear Degenerate Diffusion Equations on Bounded Domains Part I. Existence, Uniqueness and Upper Bounds

We investigate quantitative properties of nonnegative solutions u(t, x) ≥ 0 to the nonlinear fractional diffusion equation, ∂tu + LF (u) = 0 posed in a bounded domain, x ∈ Ω ⊂ R , with appropriate homogeneous Dirichlet boundary conditions. As L we can use a quite general class of linear operators that includes the two most common versions of the fractional Laplacian (−∆), 0 < s < 1, in a bounde...

Bounded Solutions for Fuzzy Integral Equations

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to tha...

Integral Equations in Nonlinear 3