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| 摘要: |
| 本文研究了一类带有扩散项的非线性抛物方程的初边值问题.利用Galerkin方法，借助Gagliardo-Nirenberg不等式、Sobolev嵌入定理和势井理论，获得了关于弱解整体存在和爆破的充分条件的结果，推广了扩散项系数为有界情形的结果. |
| 关键词: 非线性抛物方程 Galerkin方法 势井理论 整体解 爆破 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:国家自然科学基金资助（11701477）. |
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| A CLASS OF NONLINEAR PARABOLIC PROBLEMS WITH A DIFFUSION TERM |
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FAN Jia-xing,YANG Han
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| Abstract: |
| In this paper, we study the initial boundary value problem for a class of Nonlinear Parabolic Equations with a diffusion term. By means of Galerkin method, Gagliardo Nirenberg inequality, Sobolev embedding theorem and potential well theory, we obtain sufficient conditions for the global existence and blow up of weak solutions, which generalize the results for the case of bounded diffusion coefficient. |
| Key words: Nonlinear Parabolic Equation Galerkin method potential well theory global solution blow-up |
