非线性边界条件下具有变系数的热量方程解的存在性及爆破现象

李远飞; 肖胜中; 陈雪姣

doi:10.21656/1000-0887.410091

非线性边界条件下具有变系数的热量方程解的存在性及爆破现象

doi: 10.21656/1000-0887.410091

¹广东财经大学华商学院应用数学系, 广州 511300;²广东农工商职业技术学院, 广州 510507

基金项目: 广东省普通高校重点项目(自然科学)(2019KZDXM042);广东省自然科学基金(2017A030313037)

详细信息

作者简介:
李远飞(1982—),男,特聘教授,博士(通讯作者. E-mail: liqfd@163.com).

中图分类号: O178
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出版历程
- 收稿日期: 2020-02-16
- 刊出日期: 2021-01-01

Existence and Blow-Up Phenomena of Solutions to Heat Equations With Variable Coefficients Under Nonlinear Boundary Conditions

¹Department of Applied Mathematics, Huashang College, Guangdong University of Finance & Economics, Guangzhou 511300, P.R.China;²Guangdong AIB Polytechnic, Guangzhou 510507, P.R.China

摘要

摘要: 考虑了定义在Ω上的有变系数的热量方程，其中Ω∝R^N(N≥2)是一个有界的凸区域，并且方程具有非线性边界条件.利用微分不等式技术，首先推导了爆破一定发生的条件，并确定了爆破时间的上界.同时，通过对非线性项做一定的限制，得到了解的全局存在性.当爆破发生时，确定了爆破时间的下界.
- 热量方程 /
- 全局解 /
- 爆破 /
- 微分不等式
Abstract: Under nonlinear boundary conditions, the heat equations with variable coefficients defined on Ω were considered, with Ω∝R^N(N≥2) as a bounded convex region. By means of the technique of differential inequalities, the conditions under which the blowup will definitely occur were derived and the upper bound of the blowup time was determined. Meanwhile, with certain restrictions on the nonlinear terms, the global existence of the solution was obtained. At the blowup moment, the lower bound of the blowup time was also got.
- heat equation /
- global solution /
- blowup /
- differential inequality

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参考文献(25)

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