带不同幂次型非线性项的半线性三阶发展方程整体解的存在性与爆破  

Global Existence and Blow-Up for Semilinear Third Order Evolution Equation with Different Power Nonlinearities

作　　者：石金诚 刘炎[2] Shi Jincheng;Liu Yan(Department of Apllied Mathematics,Guangzhou Huashang College,Guangzhou 511300;Department of Applied Mathematics,Guangdong University of Finance,Guangzhou 510521)

机构地区：[1]广州华商学院应用数学系,广州511300 [2]广东金融学院应用数学系,广州510521

出　　处：《数学物理学报（A辑）》2024年第6期1550-1562,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(11223344);广东省自然基金(2023A1515012044);广州华商学院科研团队(2021HSKT01);广州华商学院科研项目(热弹性力学方程组的定性性态研究:2024HSTS09)

摘　　要：该文研究了一类带不同幂次型非线性项的半线性三阶发展方程的Cauchy问题,其线性化模型来自于考虑Fourier法则的经典热弹性板方程组.首先,通过适当的远离渐近线的Lr--Lq估计并结合Banach不动点原理,得到了在小初值条件下整体解的存在性;其次,对于满足特定条件的非线性项,利用检验函数法证明了解的爆破;最后,基于这些研究结果,得出该半线性三阶模型的一些临界指标.This paper studies the Cauchy problem of a class of semilinear third-order evolution equations with different power-type nonlinear terms.Its linearized model is derived from the classical thermoelastic plate equations considering Fourier's law.Firstly,by using the appropriate Lr−Lq estimation away from the asymptote and combining with the Banach fixed point theorem,the existence of the global solution under small initial conditions is obtained.Secondly,for the nonlinear terms that satisfy specific conditions,the explosion of the solution is proved by the test function method.Finally,based on these research results,some critical indicators of the semilinear third-order model are obtained.

关 键 词：整体解的存在性 半线性三阶发展方程 爆破 热弹性板方程组 

分 类 号：O175.2[理学—数学]