AAM  >> Vol. 4 No. 4 (November 2015)

    具非线性来源项的抛物型方程反问题研究
    An Parabolic Differential Equation Inverse Problem with a Nonlinear Source Term

  • 全文下载: PDF(445KB) HTML   XML   PP.320-325   DOI: 10.12677/AAM.2015.44040  
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作者:  

孙惠,肖翠娥:湖南城市学院数学与计算科学学院,湖南 益阳

关键词:
非线性抛物型方程正问题存在性唯一性反问题拟解Nonlinear Parabolic Differential Equation Direct Problem Existence Uniqueness Inverse Problem Quasi-Solution

摘要:
本文主要研究一类具非线性来源项的抛物型方程,利用单调算子理论和Sobolev嵌入定理,证明了正问题解的存在性与唯一性。在合适的容许集中证明了反问题拟解的存在性。

This paper is devoted to a class of inverse problem for parabolic differential equation with a non-linear source term. Using the theories of monotone operator and the Sobolev embedding theorem, we verify the existence and uniqueness of weak solution for the direct problem as well as the ex-istence of quasi-solutions of the inverse source problem in an appropriate class of admissible source functions.

文章引用:
孙惠, 肖翠娥. 具非线性来源项的抛物型方程反问题研究[J]. 应用数学进展, 2015, 4(4): 320-325. http://dx.doi.org/10.12677/AAM.2015.44040

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