Existence Results for a Nonlinear Transport Equation with Unbounded Admissible Velocities Space

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• 作者：M. Boumhamdi ; K. Latrach ; A. Zeghal
• 关键词：Multi ; dimensional nonlinear transport equations ; fixed point theorems ; Dunford–Pettis operators ; measure of weak noncompactness
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：13
• 期：5
• 页码：3155-3171
• 全文大小：605 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

In this paper, we discuss existence results for the nonlinear boundary value problem (1.1)–(1.2) on \({L^{1}}\)-spaces. This problem was already considered in Latrach and Zeghal (J Appl Math Comp 219:1163–1172, 2012) under the hypothesis that the velocity space has finite measure. This condition was used to establish a compactness result necessary to use fixed point theorems. In this work we show that this hypothesis is not necessary and it can be relaxed. Our analysis uses a new measure of weak noncompactness adapted to the problem, the concept of Dunford–Pettis operators and a new version of Darbo’s fixed point theorem.