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
DOI: 10.12677/AAM.2015.44040, PDF,    国家自然科学基金支持
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。
Abstract: 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

参考文献

[1] Xiao, C.E., Liu, J.B. and Liu, Y.L. (2011) An Inverse Pollution Problem in Porous Media. Applied Mathematics and Com-putation, 218, 3649-3653. http://dx.doi.org/10.1016/j.amc.2011.09.006 [Google Scholar] [CrossRef] 
[2] 李景. 不适定问题的正则化方法[D]: [博士学位论文]. 长沙: 中南大学, 2009.
[3] Liu, Z.H. and Wang, B.Y. (2009) Coefficient Identification in Parabolic Equa-tions. Applied Mathematics and Computation, 209, 379-390. http://dx.doi.org/10.1016/j.amc.2008.12.062 [Google Scholar] [CrossRef] 
[4] Hua, O.Y., Hasanov, A. and Hai, L.Z. (2008) Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations. Acta Mathematica Sinica, English Series, 24, 1617-1624. http://dx.doi.org/10.1007/s10114-008-6384-0 [Google Scholar] [CrossRef] 
[5] Liu, Z.H. (2000) On the Solvability of Degenerate Quasilinear Parabolic Equations of Second Order. Acta Mathematica Sinica, 16, 313-324. http://dx.doi.org/10.1007/s101140000052 [Google Scholar] [CrossRef] 
[6] Liu, Z.H. (2005) On Doubly Degenerate Quasilinear Parabolic Equations of Higher Order. Acta Mathematica Sinica, 21, 197-208. http://dx.doi.org/10.1007/s10114-004-0415-2 [Google Scholar] [CrossRef] 
[7] Liu, Z.H. (1999) Identification of Parameters in Semilinear Parabolic Equations. Acta Mathematica Scientia, 19, 175- 180.
[8] Zeidler, E. (1990) Nonlinear Functional Analysis and Its Applications II A/B. Springer, New York.
[9] Tikhonov, A. and Arsenin, V. (1977) Solutions of Ill-Posed Problems. Wiley, New York.

为你推荐