| 一类带非局部源的反应扩散方程解的整体存在与爆破 |
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| 引用本文： | 赵阳洋,崔泽建. 一类带非局部源的反应扩散方程解的整体存在与爆破[J]. 西南师范大学学报(自然科学版), 2019, 44(8): 34-38 |
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| 作者姓名： | 赵阳洋 崔泽建 |
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| 作者单位： | 西华师范大学数学与信息学院 |
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| 基金项目： | 国家自然科学基金项目（11301419）；西华师范大学英才科研项目（17YC382）. |
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| 摘 要： | 研究了一类具有非局部内吸收和带有非线性Neumann边界条件的拟线性反应扩散方程的整体解和爆破解.通过构造出适当的辅助函数,利用改进的微分不等式技巧,首先得到了整体解存在的充分条件,然后研究了解在有限时间的爆破,同时得到了解的爆破时间t~*的上界和下界估计.
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| 关 键 词： | 反应扩散方程 爆破 非线性Neumann边界条件 非局部内吸收 |
| 收稿时间： | 2019-04-11 |
On Existence of Global Solutions and Blow-up of a Nonlocal Reaction-Diffusion Equation |
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| ZHAO Yang-yang,CUI Ze-jian. On Existence of Global Solutions and Blow-up of a Nonlocal Reaction-Diffusion Equation[J]. Journal of southwest china normal university(natural science edition), 2019, 44(8): 34-38 |
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| Authors: | ZHAO Yang-yang CUI Ze-jian |
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| Affiliation: | College of Mathematics and Information, West China Normal University, Nanchong Sichuan 637002, China |
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| Abstract: | In this paper, an initial-boundary value problem has been investigated for a quasilinear reaction-diffusion equation with weighted nonlocal inner absorption and nonlinear Neumann boundary condition. We establish, respectively, first, sufficient conditions for the existence of global solutions are obtained, and second, the blow-up in finite time is studied and the upper and lower bounds of the blow-up time t* are obtained. |
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| Keywords: | reaction-diffusion equation blow-up Neumann boundary condition nonlocal inner absorption |
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