Existence results on the semiinfinite interval for first and second order integrodifferential equations in Banach spaces with nonlocal conditions
In this paper we prove an existence theorem for the Hammerstein integral equation , where the integral is taken in the sense of Pettis. In this theorem continuity assumptions for f are replaced by weak sequential continuity and the compactness condition is expressed in terms of the measures of weak noncompactness. Our equation is considered in general Banach spaces.
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...
Galerkin discretizations of integral equations in require the evaluation of integrals where S(1),S(2) are d-simplices and g has a singularity at x = y. We assume that g is Gevrey smooth for xy and satisfies bounds for the derivatives which allow algebraic singularities at x = y. This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules using N function evaluations of g which achieves exponential convergence |I – | ≤C exp(–rNγ) with...
In this paper we study the asymptotic behavior of a system composed of an integro-partial differential equation that models the longitudinal oscillation of a beam with a memory effect to which a thermal effect has been given by the Green-Naghdi model type III, being physically more accurate than the Fourier and Cattaneo models. To achieve this goal, we will use arguments from spectral theory, considering a suitable hypothesis of smoothness on the integro-partial differential equation.