On the existence of a local solution for an integro-differential equation with an integral boundary condition

Numerical solution for a class of parabolic integro-differential equations subject to integral boundary conditions

“…Considerable work has been made on the area of nonlocal boundary values problems in the numerical and theoretical aspects. Indeed theoretical studies devoted to these classes of problems are usually connected with some difficulties due to the presence of an integral terms in the boundary conditions, this promoted researchers to perform some modifications and improvements on the classical methods to overcome this issue (see, e.g., [2,3,12,16]).…”

Solvability and Blow-up of Solutions of Semi Linear Parabolic Problem with Integral Condition of Second Type

“…Mathematical modeling of problems with integral conditions is encountered in plasma physics (particle diffusion processes in a turbulent plasma) [29], heat transmission theory ( [4], [7]− [8], [11], [20], [21]− [22], [36], [37]), thermo-elasticity ( [23], [38], [27]− [28]), some technological processes [24], middle oscillations [13], groundwater dynamics [25], [30], moisture spread [25], chemical engineering [6], Semiconductor [3], demographic models [5] and in mathematical problems in biology [26]. Also, the integral conditions are also used for the inverse problems of the theory of thermal conduction ([9]− [10], [12], [14]− [17], [18]).…”