| 摘要: |
| 本文研究了局部有限图上无界拉普拉斯算子非线性抛物方程ut=Δu+h(x)f(u(x,t))解的存在性和爆破问题.首先利用巴拿赫不动点定理证明了温和解在短时间内的存在唯一性;其次,通过巧妙地构造辅助函数,在图满足多项式增长条件和f满足适当的条件下,利用热核估计证明了温和解会在有限时间内爆破.推广了文献[13]的结果. |
| 关键词: 无界拉普拉斯算子 爆破 抛物方程 |
| DOI： |
| 分类号:O175.26 |
| 基金项目: |
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| THE EXISTENCE OF SOLUTIONS AND BLOW-UP PHENOMENON TO THE PARABOLIC EQUATION FOR UNBOUNDED LAPLACIANS ON THE GRAPHS |
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ZHU Liping, HUANG Dawei
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College of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China
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| Abstract: |
| In this paper, we study the existence and blow-up of solutions to a nonlinear parabolic equation with unbounded Laplace operators on locally finite graphs: ut=Δu+h(x)f(u(x,t)). First, the existence and uniqueness of mild solutions in a short time interval are established using the Banach fixed-point theorem. Then, by skillfully constructing auxiliary functions and under appropriate conditions concerning polynomial growth of the graph and the nonlinearity f, the finite-time blow-up of mild solutions is proved via heat kernel estimates. These results extend those in the literature [13]. |
| Key words: unbounded Laplacians operator blow-up parabolic equation |
