带有梯度项的退化抛物方程的爆破 |
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引用本文: | 唐树乔.带有梯度项的退化抛物方程的爆破[J].数学的实践与认识,2014(5). |
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作者姓名: | 唐树乔 |
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作者单位: | 毫州师范高等专科学校; |
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基金项目: | 中央财政支持项目省级特色专业(亳州师专数学教育专业)建设点;安徽省自然科学课题(KJ2013Z217,KJ2011Z258);江苏省基础研究计划(自然科学基金)-面上项目(BK2010404);亳州师专科研课题(BZSZKYXM201111) |
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摘 要: | 考虑了带有梯度项和变指标项的非线性退化抛物方程u_t=△u~m+μ|▽u|~(p(x))(μ0)非负解的爆破性质.使用特征函数方法和不等式技巧,得到了其齐次Dirichlet问题非负解在有限时刻爆破的充分条件.
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关 键 词: | 梯度项 变指标 退化抛物方程 爆破 |
Blow-up for a Degenerate Parabolic Equation with a Gradient Term |
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Abstract: | The blow-up behavior of nonnegative solutions is studied to the following nonlinear degenerate parabolic equation:u_t = △u~m + μ|▽ u|~(p(x))(μ > 0)with a gradient term and variable exponent.By using the eigenfunction method and inequality technique on it,the sufficient condition for blow-up nonnegative solutions of the equation with homogeneous Dirichlet boundary condition is obtained. |
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Keywords: | gradient term variable exponent degenerate parabolic equation blow-up |
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