一类含有平方梯度项的塑性流体数学模型正解的存在性及正则性

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东北电力大学学报 ›› 2018, Vol. 38 ›› Issue (4) : 90-93.

数学·物理·化学

一类含有平方梯度项的塑性流体数学模型正解的存在性及正则性

侯冰, 张大鹏, 徐中海

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Existence and Regularity of Nonnegative Solution of Mathematical Model of A Plastic Fluid with Square Gradient Terms

Hou Bing, Zhang Dapeng, Xu Zhonghai

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摘要

考虑塑性流体的下列边界退化椭圆问题

经典解的存在性及其正则性，其中：Ω={（x，y）：x²+y² < r₀²}⊂R²，f₁（t）是定义在（-∞，+∞）上的非负且严格单调递增的光滑函数，g（t）和f（t）是定义在（0，+∞）上的非负且严格单调递减的光滑函数.应用正则化技术及精细的估计技巧，在一定条件下得到了问题（P）经典解的存在性及其正则性.显然，得到的结果比经典的结果更好.

Abstract

In this paper,we considered the singular quasi-linear anisotropic elliptic boundary value problem

where Ω={(x,y):x²+y²<r₀²}⊂R². Clearly,this is a boundary degenerate elliptic problem. We show that the solution of the Dirichlet boundary value problem (P) was smooth in the interior and Lipschitz continuous up to the degenerate boundary. The regularity of solution of the problem (P) is more sharper than classical theory.

导出引用

侯冰, 张大鹏, 徐中海. 一类含有平方梯度项的塑性流体数学模型正解的存在性及正则性. 东北电力大学学报. 2018, 38(4): 90-93

Hou Bing, Zhang Dapeng, Xu Zhonghai. Existence and Regularity of Nonnegative Solution of Mathematical Model of A Plastic Fluid with Square Gradient Terms. Journal of Northeast Electric Power University. 2018, 38(4): 90-93

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吉林省自然科学基金（20150101002JC）

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2018-02-13	2018-08-30
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