一类均匀内热源对流问题的稳定性界
Stability bounds in a problem of convection with uniform internal heat source
摘要：
大气运动和地幔对流是由内热源引起的自然对流现象中的两种。它们由于失去稳定性而从导电状态分叉。尽管它们的重要性，由于发生的变系数的非线性偏微分方程的基本平衡周围的扰动的演变，到目前为止，这些现象主要是处理数值和实验。没有严格的研究是已知的。在本文中，我们实现了第一次这样的线性研究的特征值问题与这些方程的对流问题与均匀的内部热源在水平流体层由两个刚性壁的边界。我们的方法使用傅里叶级数展开的未知函数。数值结果和图表给出显示的热源的存在下的不稳定的影响。
英文摘要：
Motion in the atmosphere or mantle convection are two among phenomena of natural convection induced by internal heat sources. They bifurcate from the conduction state as a result of its loss of stability. In spite of their importance, due to the occurrence of variable coefficients in the nonlinear partial differential equations governing the evolution of the perturbations around the basic equilibrium, so far these phenomena were treated mostly numerically and experimentally. No rigorous study is known. In this paper we realize for the first time such a linear study for the eigenvalue problem associated with those equations for a convection problem with an uniform internal heat source in a horizontal fluid layer bounded by two rigid walls. Our method uses Fourier series expansions for the unknown functions. Numerical results and graphs are given showing a destabilizing effect of the presence of the heat source.
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