Variational theory for the shallow water problem

Variational Principle for the Generalized KdV-Burgers Equation with Fractal Derivatives for Shallow Water Waves

The unsmooth boundary will greatly affect motion morphology of a shallow water wave, and a fractal space is introduced to establish a generalized KdV-Burgers equation with fractal derivatives. The semi-inverse method is used to establish a fractal variational formulation of the problem, which provides conservation laws in an energy form in the fractal space and possible solution structures of t...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Nonlinear edge waves and shallow-water theory

Cauchy problem for viscous rotating shallow water equations

We consider the Cacuhy problem for a viscous compressible rotating shallow water system with a third-order surface-tension term involved, derived recently in the modelling of motions for shallow water with free surface in a rotating sub-domain [18]. The global existence of the solution in the space of Besov type is shown for initial data close to a constant equilibrium state away from the vacuu...

A shallow-water theory for annular sections of Keplerian Disks

Context. A scaling argument is presented that leads to a shallow water theory of non-axisymmetric disturbances in annular sections of thin Keplerian disks. Aims. To develop a theoretical construction that will aid in physically understanding the relationship of known twodimensional vortex dynamics to their three-dimensional counterparts in Keplerian disks. Methods. Using asymptotic scaling argu...