关键词: stochastic optimal control, reflected diffusion with jumps, Hamilton-Jacobi-Bellman equation, viscosity solution, Oldroyd fluid B, non-Newtonian fluid, time dependent flow, variational-analytical approach, improved approach dut to Kantorovich

Abstract: In the present investigation the time dependent flow of an Oldroyd fluid B in ahorizontal eylindrical pipe is stuided by the variational analytical approach developed by author. The tome dependent problem is mathematically reduced to a partial differential equation of third order. Using the improved variational approach due to Kantorovich the partial differential equation can be reduced to a system of ordinary differential equations for different approximations. The ordinary differential equations are solved by the method of the Laplace transform which is led to an analytical formof the solutions.

Key words: stochastic optimal control, reflected diffusion with jumps, Hamilton-Jacobi-Bellman equation, viscosity solution, Oldroyd fluid B, non-Newtonian fluid, time dependent flow, variational-analytical approach, improved approach dut to Kantorovich