A STRONGLY ILL-POSED INTEGRO-DIFFERENTIAL PARABOLIC PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS

Linear Advection with Ill-posed Boundary Conditions via L-minimization

The goal of this paper is to explain a phenomenon that has been reported in [4]; namely, finite-element-based best L-approximations seem to converge to viscosity solutions of some classes of first-order PDE’s. In particular we prove in this paper that it is indeed the case in dimension one for the linear transport equation equipped with a set of ill-posed boundary conditions. To explain our int...

Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary conditions

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University P.O. Box 80203, Jeddah 21589, Saudi Arabia Full list of author information is available at the end of the article Abstract This article investigates a boundary value problem of Riemann-Liouville fractional integro-differential equations with fractional nonlocal integral boundary condi...

Nonlinear boundary value problems for first order integro-differential equations with impulsive integral conditions∗

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.

On a parabolic problem with nonlinear Newton boundary conditions

The paper is concerned with the study of a parabolic initial-boundary value problem with nonlinear Newton boundary condition considered in a two-dimensional domain. The goal is to prove the existence and uniqueness of a weak solution to the problem in the case when the nonlinearity in the Newton boundary condition does not satisfy any monotonicity condition and to analyze the finite element app...

Second-Order Boundary Value Problem with Integral Boundary Conditions