By means of three fundamental structures we can define, in a general way, a sheaf A of differential algebras containing most of the special cases met in the theory of generalized functions. A convenient choice of these structures permits us to study Burgers’ equation with δ-Dirac measure as initial data, and we can construct a generalized δ-shock wave as an approximate solution, self-similar to...

Waves with constant, nonzero linearized frequency form an interesting class of nondispersive waves whose properties differ from those of nondispersive hyperbolic waves. We propose an inviscid Burgers-Hilbert equation as a model equation for such waves, and give a dimensional argument to show that it models Hamiltonian surface waves with constant frequency. Using the method of multiple scales, w...

There are presented the investigations in the framework of pseudoanalysis semirings whose operations are generated with functions of one variable. Based on the operations with generators there was developed a theory of generalized functions in analogy to the Mikusiński’s operators, which enables the construction of a generalized solution of the Burgers equation. There are considered extensions ...

In this paper, we investigate the asymptotic behavior of solutions to Cauchy problem with far field condititon for generalized Benjamin–Bona–Mahony–Burgers equation a fourth-order dissipative term. When corresponding Riemann hyperbolic part admits solution which consists single rarefaction wave, it is proved that tends toward wave as time goes infinity. We can further obtain same global stabili...

Higher-order accurate finite-difference schemes for solving the unsteady Burgers’ equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented. The unsteady Burgers’ equation belongs to a few nonlinear partial differential equations which has an exact solution, and it allows one to compare the numerical solution with the exact one, and the properti...

An analysis is made to see the influences of Hall current on the flow of a Burgers’ fluid. The velocity field corresponding to flow in a pipe is determined. The closed form analytical solutions for several Newtonian and non-Newtonian fluid models can be obtained from the present analysis as the limiting cases. MIRAMARE – TRIESTE December 2005 Corresponding author: mkhan−[email protected] Junior Asso...

In our research work, we have developed a model describing the characteristics of bio-convection and moving microorganisms in flows magnetized generalized Burgers’ nanoliquid with Fourier’s Fick’s laws stretchable sheet. Considerations been made to Cattaneo–Christov mass heat diffusion theory. According relation, Buongiorno phenomenon for motion fluid has also applied. Similarity transformation...