Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

Lili Chen

doi:http://dx.doi.org/10.26855/jamc.2022.03.005

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Article Open Access http://dx.doi.org/10.26855/jamc.2022.03.005

Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

Lili Chen

Department of Mathematics, Shandong Normal University, Jinan 250014, Shandong, China.

*Corresponding author: Lili Chen

Published: February 22,2022

Abstract

This paper mainly studies the large time behavior of two-dimensional isothermal spherically symmetric compressible Euler-Poisson equations with variable coefficient damping in a bounded region. This equation and its variants have been used to describe the dynamic behavior of many important physical flows including the propagation of electrons in submicron semiconductor devices, the biological transport of ions for channel proteins, the motion of stars in the theory of general relativity and so on. This paper mainly proves that the weak solution converges exponentially to the unique stationary solution in time. The main methods are entropy estimation and energy method. Here, the key step is to construct an appropriate entropy estimation to cooperate with the energy method to obtain that when t→∞, the spherically symmetric weak solution of the isothermal spherically symmetric Euler-Poisson equations with variable coefficient damping converges to the unique smooth solution of the corresponding stationary equations at an exponential rate under the condition that the corresponding initial values are satisfied.

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How to cite this paper

Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

How to cite this paper: Lili Chen. (2022) Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping. Journal of Applied Mathematics and Computation, 6(1), 24-29.

DOI: http://dx.doi.org/10.26855/jamc.2022.03.005

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Large Time Behavior of Entropy Solutions to Two-Dimensional Unipolar Hydrodynamic Model for Semiconductor Devices with Variable Coefficient Damping

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