应用数学2025，Vol.38Issue(3)：691-702,12.
一类混合型非线性发展方程解的局部存在性探究
Investigating Solutions in Nonlinear Evolution Equations:A Focus on Local Existence in Mixed Types
摘要
Abstract
With the urgent need to resolve complex behaviors in nonlinear evolution equations,this study makes a contribution by establishing the local existence of solutions for Cauchy problems associated with equations of mixed types.Our primary contribution is the establishment of solution existence,illuminating the dynamics of these complex equations.To tackle this challenging problem,we construct an approximate solution sequence and apply the contraction mapping principle to rigorously prove local solution existence.Our results significantly advance the understanding of nonlinear evolution equations of mixed types.Furthermore,they provide a versatile,powerful approach for tackling analogous challenges across physics,engineering,and applied mathematics,making this work a valuable reference for researchers in these fields.关键词
非线性发展方程/压缩映像/Sobolev空间/扩散系统Key words
Nonlinear evolution equation/Contraction mapping principle/Sobolev space/Dissipative system分类
数学引用本文复制引用
涂雨秋,樊龙,达后..一类混合型非线性发展方程解的局部存在性探究[J].应用数学,2025,38(3):691-702,12.基金项目
Supported by the National Natural Science Foundation of China(12201368,62376252),Key Project of Natural Science Foundation of Zhejiang Province(LZ22F030003) （12201368,62376252）
Zhejiang Province Leading Geese Plan(2024C02G1123882,2024C01SA100795). （2024C02G1123882,2024C01SA100795）
