Existence and blowup of solutions for the modified Klein-Gordon-Zakharov equations for plasmas with a quantum correction

Advances in Difference Equations

Shaomei Fang¹  Changhong Guo² 

[1] Department of Mathematics, South China Agricultural University, Guangzhou, P.R. China;School of Management, Guangdong University of Technology, Guangzhou, P.R. China

关键词: existence and blowup;    modified Klein-Gordon-Zakharov equations;    quantum correction;    dilation transformation;   

DOI  :  10.1186/s13662-017-1357-1

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

This paper studies the existence and blowup of solutions for the modified Klein-Gordon-Zakharov equations for plasmas with a quantum correction, which describe the interaction between high frequency Langmuir waves and low frequency ion-acoustic waves in a plasma considering the quantum effects. Firstly the existence and uniqueness of the local smooth solutions are obtained by the a priori estimates and the Galerkin method. Secondly, and what is more, by introducing some auxiliary functionals and invariant manifolds, the authors study and derive a sharp threshold for the global existence and blowup of solutions by applying potential well argument and the concavity method. Furthermore, two more specific conditions of how small the initial data are for the solutions to exist globally are concluded by the dilation transformation.

【 授权许可】

CC BY