| 具测度初值的非线性抛物方程组的Cauchy问题 |
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| 引用本文： | 宋萌萌,尚海锋. 具测度初值的非线性抛物方程组的Cauchy问题[J]. 山东大学学报(理学版), 2016, 51(10): 41-47. DOI: 10.6040/j.issn.1671-9352.0.2015.613 |
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| 作者姓名： | 宋萌萌 尚海锋 |
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| 作者单位： | 河南理工大学数学与信息科学学院, 河南 焦作 454000 |
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| 基金项目： | 国家自然科学基金青年基金资助项目(11201124);河南省高等学校青年骨干教师资助计划(2015GGJS-070);河南理工大学杰出青年基金资助项目(J2014-03) |
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| 摘 要： | 研究了一类具强耦合源的退化抛物方程组的Cauchy问题,其中初值为Radon测度。当指标满足一定范围时,克服了方程退化性与强耦合源同时存在带来的困难, 从而得到了解的存在性。还进一步证明了指标的限制范围对解的存在性来说是最优的。
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| 关 键 词： | 抛物方程组 Cauchy问题 测度初值 耦合非线性源 |
| 收稿时间： | 2015-12-17 |
Cauchy problem for nonlinear parabolic equation systems with initial data measures |
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| SONG Meng-meng,SHANG Hai-feng. Cauchy problem for nonlinear parabolic equation systems with initial data measures[J]. Journal of Shandong University, 2016, 51(10): 41-47. DOI: 10.6040/j.issn.1671-9352.0.2015.613 |
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| Authors: | SONG Meng-meng SHANG Hai-feng |
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| Affiliation: | School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, Henan, China |
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| Abstract: | The Cauchy problem for a class of degenerate parabolic system with strongly coupling source is studied, where initial data are measured. When the known parameters satisfy some conditions, the difficulties are avoided which come from the interactions between the degeneracy of the principal and the strongly coupling source, and the existence of solutions is obtained. Moreover, it is proved that these conditions are optimal for the existence of solutions. |
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| Keywords: | parabolic equation system Cauchy problem measures as initial data coupling nonlinear source |
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