具有空间相关阻尼的双极Euler-Poisson方程解的长时间行为
Large-time behavior of solutions to bipolar Euler-Poisson equations with space-dependent damping
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中文总结 AI 辅助
本文通过加权能量方法证明，在空间相关阻尼下，一维双极Euler-Poisson方程Cauchy问题的小扰动初值存在唯一全局光滑解，并以与常数阻尼相同的代数速率收敛到稳态，且无需阻尼系数的小性条件。
中文摘要 AI 辅助
本文研究一维双极Euler-Poisson方程在空间相关阻尼下的Cauchy问题，该方程出现在半导体的流体动力学模型中。值得注意的是，两个压力函数允许不同，且掺杂分布非零。通过精心选择权重的加权能量方法，我们证明：若常数稳态附近的初始扰动足够小，则Cauchy问题存在唯一的全局光滑解，该解以代数衰减速率收敛到常数稳态。我们证明这些衰减速率与常数系数阻尼情形下已建立的衰减速率一致，从而克服了空间相关阻尼对解的衰减速率的影响。一个关键特征是无需对空间相关阻尼系数施加小性条件。
英文摘要
This paper is concerned with the Cauchy problem for the one-dimensional bipolar Euler-Poisson equations with space-dependent damping, which arise in the hydrodynamic model of semiconductors. Notably, the two pressure functions are allowed to be different, and the doping profile is nonzero. By means of the time-weighted energy method with carefully chosen weights, we prove that if the initial perturbation around a constant steady-state is small enough, the Cauchy problem admits a unique global smooth solution, which converges to the constant steady-state at algebraic decay rates. We show that the decay rates coincide with those established for the constant-coefficients damping case, thereby overcoming the influence of spatially dependent damping on the decay rates of the solutions. A key feature is that no smallness of the space-dependent damping coefficients is required.
发表机构
- School of Mathematics, Jilin University（吉林大学数学学院）
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