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Error estimates for the time discretization of a semilinear integrodifferential parabolic problem with unknown memory Kernel

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Abstract
This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel. This equation is accompanied by a Robin boundary condition. The missing kernel can be recovered from an additional global measurement in integral form. In this contribution, an error analysis is performed for a time-discrete numerical scheme based on Backward Euler's Method. The theoretical results are supported by some numerical experiments.
Keywords
Parabolic inverse problem, convolution kernel, error estimates, CONVOLUTION KERNEL, INVERSE PROBLEMS, RECONSTRUCTION

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MLA
Grimmonprez, Marijke, Karel Van Bockstal, and Marian Slodicka. “Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel.” NUMERICAL MATHEMATICS : THEORY, METHODS AND APPLICATIONS 10.1 (2017): 116–144. Print.
APA
Grimmonprez, M., Van Bockstal, K., & Slodicka, M. (2017). Error estimates for the time discretization of a semilinear integrodifferential parabolic problem with unknown memory Kernel. NUMERICAL MATHEMATICS : THEORY, METHODS AND APPLICATIONS, 10(1), 116–144.
Chicago author-date
Grimmonprez, Marijke, Karel Van Bockstal, and Marian Slodicka. 2017. “Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel.” Numerical Mathematics : Theory, Methods and Applications 10 (1): 116–144.
Chicago author-date (all authors)
Grimmonprez, Marijke, Karel Van Bockstal, and Marian Slodicka. 2017. “Error Estimates for the Time Discretization of a Semilinear Integrodifferential Parabolic Problem with Unknown Memory Kernel.” Numerical Mathematics : Theory, Methods and Applications 10 (1): 116–144.
Vancouver
1.
Grimmonprez M, Van Bockstal K, Slodicka M. Error estimates for the time discretization of a semilinear integrodifferential parabolic problem with unknown memory Kernel. NUMERICAL MATHEMATICS : THEORY, METHODS AND APPLICATIONS. 2017;10(1):116–44.
IEEE
[1]
M. Grimmonprez, K. Van Bockstal, and M. Slodicka, “Error estimates for the time discretization of a semilinear integrodifferential parabolic problem with unknown memory Kernel,” NUMERICAL MATHEMATICS : THEORY, METHODS AND APPLICATIONS, vol. 10, no. 1, pp. 116–144, 2017.
@article{8510780,
  abstract     = {This paper is devoted to the study of an inverse problem containing a semilinear integrodifferential parabolic equation with an unknown memory kernel. This equation is accompanied by a Robin boundary condition. The missing kernel can be recovered from an additional global measurement in integral form. In this contribution, an error analysis is performed for a time-discrete numerical scheme based on Backward Euler's Method. The theoretical results are supported by some numerical experiments.},
  author       = {Grimmonprez, Marijke and Van Bockstal, Karel and Slodicka, Marian},
  issn         = {1004-8979},
  journal      = {NUMERICAL MATHEMATICS : THEORY, METHODS AND APPLICATIONS},
  keywords     = {Parabolic inverse problem,convolution kernel,error estimates,CONVOLUTION KERNEL,INVERSE PROBLEMS,RECONSTRUCTION},
  language     = {eng},
  number       = {1},
  pages        = {116--144},
  title        = {Error estimates for the time discretization of a semilinear integrodifferential parabolic problem with unknown memory Kernel},
  url          = {http://dx.doi.org/10.4208/nmtma.2017.m1513},
  volume       = {10},
  year         = {2017},
}

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