| 一类具非标准增长条件和零阶项的抛物方程的存在性结果 |
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| 引用本文： | 李仲庆. 一类具非标准增长条件和零阶项的抛物方程的存在性结果[J]. 数学研究及应用, 2023, 43(4): 467-476 |
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| 作者姓名： | 李仲庆 |
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| 作者单位： | 贵州财经大学数学与统计学院, 贵州 贵阳 550025 |
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| 基金项目： | 国家自然科学基金(Grant No.11901131), 贵州财经大学校级科研项目(Grant No.2022KYYB01). |
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| 摘 要： | 在变指数背景下,我们考虑了一类具零阶项的抛物方程解的存在性结果. 存在性的证明在本质上依赖于选取合适的检验函数,这些检验函数要同时兼顾方程右端源项的可积性和零阶项. 利用先验估计和极限分析,借助于Young测度方法确立了非线性项的弱收敛元.
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| 关 键 词： | 非标准增长条件 零阶项 弱解 |
| 收稿时间： | 2022-09-18 |
| 修稿时间： | 2023-01-08 |
Existence Result to a Class of Parabolic Equations with Nonstandard Growth Condition and Zero Order Term |
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| Zhongqing LI. Existence Result to a Class of Parabolic Equations with Nonstandard Growth Condition and Zero Order Term[J]. Journal of Mathematical Research with Applications, 2023, 43(4): 467-476 |
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| Authors: | Zhongqing LI |
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| Affiliation: | School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guizhou 550025, P. R. China |
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| Abstract: | In the setting of variable exponent, an existence result to a class of parabolic equations with zero order term is proved. The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously. By virtue of a priori estimates and some limit analyses, the weak limit of the nonlinear principal term is identified via the Young measures method. |
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| Keywords: | nonstandard growth condition zero order term weak solutions |
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