一类具非标准增长条件和零阶项的抛物方程的存在性结果

Existence Result to a Class of Parabolic Equations with Nonstandard Growth Condition and Zero Order Term

中文关键词:  非标准增长条件  零阶项  弱解

英文关键词:nonstandard growth condition  zero order term  weak solutions

中文摘要:

      在变指数背景下,我们考虑了一类具零阶项的抛物方程解的存在性结果. 存在性的证明在本质上依赖于选取合适的检验函数,这些检验函数要同时兼顾方程右端源项的可积性和零阶项. 利用先验估计和极限分析,借助于Young测度方法确立了非线性项的弱收敛元.

英文摘要:

      In the setting of variable exponent, an existence result to a class of parabolic equations with zero order term is proved. The proof of existence relies essentially on selecting some suitable test functions based upon the integrability of the source term and the zero order term simultaneously. By virtue of a priori estimates and some limit analyses, the weak limit of the nonlinear principal term is identified via the Young measures method.