Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method
Solving convection-diffusion equations with mixed, Neumann and Fourier boundary conditions and measures as data, by a duality method
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通过对偶方法以混合、诺依曼和傅里叶边界条件和测量数据求解对流扩散方程
DOI：
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发表时间：
2000
影响因子：
1.4
通讯作者：
J. Droniou
中科院分区：
文献类型：
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作者：
J. Droniou
本文在文[1]的基础上，证明了R的开子集上对流扩散方程的解的存在唯一性，并以一种测度为数据，在不同的边界条件：混合边界条件、Neumann边界条件和傅立叶边界条件下，得到了解的存在唯一性。第一部分证明了当Q<；N/(NΩ1)时，对流扩散方程在(W1，Q(−))‘中具有这些边界条件和数据的解的正则性结果。第二部分通过一个二元性技巧将这些正则性结果转化为当数据是度量时的存在唯一性结果。
In this paper, we prove, following [1], existence and uniqueness of the solutions of convection-diffusion equations on an open subset of R , with a measure as data and different boundary conditions: mixed, Neumann or Fourier. The first part is devoted to the proof of regularity results for solutions of convection-diffusion equations with these boundary conditions and data in (W 1,q(Ω))′, when q < N/(N − 1). The second part transforms, thanks to a duality trick, these regularity results into existence and uniqueness results when the data are measures.