| 摘要: |
| 针对局部有限图上无界拉普拉斯算子非线性抛物方程ut = ?u + h(x)f(u)(t, x), 本文首
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发生爆破. |
| 关键词: 无界拉普拉斯算子 爆破解 抛物方程 |
| DOI： |
| 分类号:O175.26 |
| 基金项目: |
|
| THE EXISTENCE OF SOLUTIONS AND BLOW-UP PHENOMENON TO THE PARABOLIC EQUATION FOR UNBONDEN LAPLACIANS ON THE GRAPHS |
|
Huang Dawei, Zhu Liping
|
|
College of Science, Xi’an University of Architecture and Technology
|
| Abstract: |
| For the nonlinear parabolic equation with unbounded Laplacian on locally finite
graphs ut = ?u + h(x)f(u)(t, x), this paper first establishes the existence and uniqueness of mild
solutions in a short time interval by employing the Banach fixed-point theorem. Subsequently, under
the condition that the graph satisfies polynomial growth and f meets appropriate assumptions, the
paper proves that the mild solution will blow up in finite time by ingeniously constructing auxiliary
functions and utilizing heat kernel estimates. |
| Key words: unbounded Laplacians operator blow-up solution parabolic equation |
