Asymptotic behavior of solutions of a parabolic equations in a band domain  

带状区域中一类抛物方程解的渐近行为

作　　者：DU Wenjing HUANG Xinyu WU Junyan XIU Xinxiu YUAN Lixia 杜文静;黄鑫宇;吴俊彦;修新秀;袁丽霞(上海师范大学数理学院,上海200234)

机构地区：[1]Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China

出　　处：《上海师范大学学报(自然科学版中英文)》2024年第6期719-724,共6页Journal of Shanghai Normal University(Natural Sciences)

基　　金：The National Natural Science Foundation of China(12001375)。

摘　　要：consider a quasilinear parabolic equation in a band domain with inhomogeneous and unbounded boundary conditions.We show that,under certain conditions,the solution u of the initialboundary value problem tends to infinite as t→∞.Moreover,by using the zero number argument we show that for any x≠O,u_(x)(x,t)also tends as t→∞to infinity,that is,the gradient is asymptotically unbounded.考虑带状区域中具有非均匀无界边界条件的一类拟线性抛物方程。在一定条件下,证明当时间t→∞时,初边值问题的解u趋于无穷.而且,利用零点性质还证明了:对任何x≠O,都有u_(x)(x,t)→∞,即梯度也是渐近无界的.

关 键 词：curvature flow quasilinear parabolic equation translating solution asymptotic behavior 

分 类 号：O175[理学—数学]