a simple new closed form of the green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. the result is verified by applying several examples.

We introduce a concept of differential flatness for systems described by nonlinear partial differential equations. It generalizes the now classical notion of differential flatness for finite differential systems and its recent extensions to linear partial differential equations. We apply it to the motion planning of a very flexible rod, outside of the linear approximation range.

in oil industry, spontaneous imbibition is an important phenomenon in recovery from fractured reservoirs which can be defined as spontaneous uptake of a wetting fluid into a porous solid. spontaneous imbibition involves both cocurrent and countercurrent flows. when a matrix block is partially covered by water, oil recovery is dominated by cocurrent imbibition i.e. the production of non wetting ...

Residual terms that appear in nonlinear PDEs that are constructed to generate filtered representations of the variables of the fully resolved system are examined by way of a consistency condition. It is shown that certain commonly used empirical gradient models for the residuals fail the test of consistency and therefore cannot be validated as approximations in any reliable sense. An alternate ...

and Applied Analysis 3 definition, it may happen that such a solution does not belong to any of the customary spaces of generalized functions. For example, given a function u : C \ {z0} −→ C 1.3 which is analytic everywhere except at the single point z0 ∈ C, and with an essential singularity at z0, Picard’s Theorem states that u attains every complex value, with possibly one exception, in every...

As the existence theory for solutions of nonlinear partial differential equations becomes better understood, one can begin to ask more detailed questions about the behavior of solutions of such equations. Given the bewildering complexity which can arise from relatively simple systems of ordinary differential equations, it is hopeless to try to describe fully the behavior which might arise from ...

The ultimate topic to be touched on in this book is the vast and active field of nonlinear partial differential equations. Leaving aside quantum mechanics, which remains to date an inherently linear theory, most real-world physical systems, including gas dynamics, fluid mechanics, elasticity, relativity, ecology, neurology, thermodynamics, and many more, are modeled by nonlinear partial differe...

The connection of curves and surfaces in R3 to some nonlinear partial differential equations is very well known in differential geometry [1], [2]. Motion of curves on two dimensional surfaces in differential geometry lead to some integrable nonlinear differential equations such as nonlinear Schrödinger (NLS) equation [3], Korteweg de Vries (KdV) and modified Korteweg de Vries (mKdV) equations [...