The pressure and velocity at the most constricted area of the airway decreased after RME for the laminar flow more than the turbulent flow although they both showed similar distribution patterns for the integral and partial models.
Notice that the concepts of ww-compact and ws-compact mappings arise naturally in the study of integral and partial differential equations (see [24 32]).
Pressure, velocity, and turbulent kinetic energy decreased after RME for laminar and turbulent flow, but they were similar for the integral and partial models.
Fixed-point theory has attracted many mathematicians since it provides a simple proof for the existence and uniqueness of the solutions to various mathematical models (integral and partial differential equations, variational inequalities etc).
Maximal operators play an important role in the differentiability properties of functions, singular integrals and partial differential equations.
Pseudo almost periodic functions have many applications in several problems, for example in the theory of functional differential equations, integral equations, and partial differential equations.
As for almost periodic functions, pseudo-almost periodic functions have many applications in several problems, for example, in theory of functional differential equations, integral equations, and partial differential equations.
It is clear that more complicated partial differential systems with deviated variables and partial differential integral systems can be obtained from (3) and (6) by a suitable definition of f and g.
Using a new transform method, Fokas, ben-Avraham and Antipov translate some important boundary value problems for linear and for integral nonlinear partial differential equations in physical plane to the corresponding modified Helmholtz equations.
Mathematics: Ordinary and partial differential equations, Integral equations, Asymptotics, Variational and functional-analytical methods, Numerical analysis, Computational methods.
