Universal Journal of Mathematics and Mathematical Sciences
Volume 5, Issue 1, Pages 23 - 35
(January 2014)
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ON THE APPROXIMATION OF THE SYSTEM OF EQUATIONS OF FREE CONVECTION OF VISCOUS INCOMPRESSIBLE FLOW WITH DISSIPATION ENERGY
A. Jaikbayev, S. Mukhambetzhanov and S. Janabekova
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Abstract: The initial boundary problem for equations of free convection with dissipation energy in is considered in the paper. Under the condition of certain growth of thermal conductivity coefficient as a function of temperature, the existence and uniqueness of smooth solution is established. The proof is based on a priori estimates, An e-approximation of system by evolution system is considered. The existence and uniqueness of approximate solution in the same functional spaces is proved. The convergence estimate of approximate solution to solution of initial problem is given. |
Keywords and phrases: initial boundary problem, equations of free convection with dissipation energy, thermal conductivity coefficient, existence and uniqueness, smooth solution, a priori estimates, e-approximation, convergence estimate. |
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