Multi-valued solution of the Burgers' equation and shock Determination I.

Abstract

We present the Burgers' equation as a balance between time evolution, non-linearity and dissipation and use these properties to examine the vanishing behaviour of the dissipation coefficient. Furthermore, we undertake a rigorous mathematical analysis which gives rise to multi-valued solutions after sufficient time and discontinuities. Though the complete solution is single-valued for all time, t, revelations from the equation of shock determination is interesting in the determination of the random properties of the wave.



Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 145-148