For quasilinear integro-diierential equations of the form u t ?aA(u) = f, where a is a scalar singular integral kernel that behaves like t ? , 1 2 < 1 and A is a second order quasilinear elliptic operator in divergence form, solutions are found for which A(u) is integrable over space and time.

We review some regularity results for integro-differential equations, focusing on Hölder estimates for equations with rough kernels and their applications. We show that if we take advantage of the integral form of the equation, we can obtain simpler proofs than for second order equations. For the equations considered here, the Harnack inequality may not hold. Mathematics Subject Classification ...

In the present work we discuss the existence of solutions for a system of nonlinear fractional integro-differential equations with initial conditions. This system involving the Caputo fractional derivative and Riemann−Liouville fractional integral. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.

Department of Mathematics and Sciences Dhofar University, Salalah Oman [email protected] Abstract Legendre wavelets methods are commonly used for the numerical solution of integral equations. In this paper, we apply the Legendre wavelets method to approximate the solution of fractional integro-differential equations. Numerical examples are also presented to demonstrate the validity of the method....

This paper is concerned with the nonlinear boundary value problems for first order integro-differential equations with impulsive integral conditions. By using of the method of lower and upper solutions coupled with the monotone iterative technique, we give conditions for the existence of extremal solutions.

In this paper we study an integro-differential equation describing granular flow dynamics with slow erosion. This nonlinear partial differential equation is a conservation law where the flux contains an integral term. Through a generalized wave front tracking algorithm, approximate solutions are constructed and shown to converge strongly to a Lipschitz semigroup.

In these appendices we present, successively, I conditions for the existence of a unique solution of (1.1) and (1.2); II three tables of coefficients of forward differentiation formulas, and of two common LM formulas for ODEs, viz., backward differentiation formulas and Adams-Moulton formulas; III two lemmas which are needed in: IV proofs of the main results of this paper, as far as they are no...

This paper investigates the existence and asymptotic behavior of solutions for weighted p t Laplacian integro-differential system with multipoint and integral boundary value condition in half line. When the nonlinearity term f satisfies subp− − 1 growth condition or general growth condition, we give the existence of solutions via Leray-Schauder degree. Moreover, the existence of nonnegative sol...

Saccharomyces cerevisiae (baker’s yeast) can exhibit sustained oscillations during the operation in a continuous bioreactor that adversely affects its stability and productivity. Because of heterogeneous nature of cell populations, the cell population balance equation (PBE) can be used to capture the dynamic behavior of such cultures. In this work, an unstructured-segregated model is used f...