Existence And Prolonged Overall Behavior Of Entropy Euler-Poisson Equations And Other Non-bipolar

In this paper, we study the one-dimensional bipolar non-isentropicEuler-Poisson equations which can model various physical phenomena, such as thepropagation of electron and hole in submicron semiconductor devices, thepropagation of positive ion and negative ion in plasmas, and the biological transportof ions for channel proteins. We show the existence and large time behavior of globalsmooth solutions, when the difference of two particles’ initial mass is non-zero, andthe far field of two particles’ initial temperatures is not the ambient devicetemperature. we will introduce a series of the perturbed variants by making aperturbation of our studied systems to the nonlinear diffusion waves. And bydiscussing the perturbed variants, we can prove our results. But in the case discussedin this paper, the perturbed variants is not zero at the far fields x=±∞if we onlymake a perturbation of our studied equations to the nonlinear diffusion waves. Inorder to overcome this difficulty, we ingeniously construct some new correctionfunctions. Then, we establish some crucial energy estimates. By using the continuityargument, we can prove our results. This result improves that of [Y.-P. Li J. D. E.250(2011),1285-1309] for the case that the difference of two particles’ initial mass iszero, and the far field of the initial temperature is the ambient device temperature.