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On a finite difference scheme for an inverse integro-differential problem using semigroup theory: a functional analytic approach

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Abstract
The problem of reconstructing an unknown memory kernel from an integral overdetermination in an abstract linear (of convolution type) evolution equation of parabolic type is considered. After illustrating some results of existence and uniqueness of a solution for the differential problem, we study its approximation by Rothe's method. We prove a result of stability and another concerning the order of approximation of the solution in dependence of its regularity. The mail tool is a maximal regularity result for solutions to abstract parabolic finite difference schemes. Two model problems to which the results are applicable are illustrated.
Keywords
Rothe’s method, semigroup theory, Convolution kernel, inverse problem, SEMILINEAR PARABOLIC PROBLEM, CONVOLUTION KERNEL, WAVE-EQUATION, MEMORY, RECONSTRUCTION, IDENTIFICATION, SPACES, SOBOLEV, BESOV, MODEL

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MLA
De Staelen, Rob, and Davide Guidetti. “On a Finite Difference Scheme for an Inverse Integro-differential Problem Using Semigroup Theory: a Functional Analytic Approach.” NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 37.7 (2016): 850–886. Print.
APA
De Staelen, R., & Guidetti, D. (2016). On a finite difference scheme for an inverse integro-differential problem using semigroup theory: a functional analytic approach. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 37(7), 850–886.
Chicago author-date
De Staelen, Rob, and Davide Guidetti. 2016. “On a Finite Difference Scheme for an Inverse Integro-differential Problem Using Semigroup Theory: a Functional Analytic Approach.” Numerical Functional Analysis and Optimization 37 (7): 850–886.
Chicago author-date (all authors)
De Staelen, Rob, and Davide Guidetti. 2016. “On a Finite Difference Scheme for an Inverse Integro-differential Problem Using Semigroup Theory: a Functional Analytic Approach.” Numerical Functional Analysis and Optimization 37 (7): 850–886.
Vancouver
1.
De Staelen R, Guidetti D. On a finite difference scheme for an inverse integro-differential problem using semigroup theory: a functional analytic approach. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION. Taylor & Francis; 2016;37(7):850–86.
IEEE
[1]
R. De Staelen and D. Guidetti, “On a finite difference scheme for an inverse integro-differential problem using semigroup theory: a functional analytic approach,” NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, vol. 37, no. 7, pp. 850–886, 2016.
@article{7186074,
  abstract     = {{The problem of reconstructing an unknown memory kernel from an integral overdetermination in an abstract linear (of convolution type) evolution equation of parabolic type is considered. After illustrating some results of existence and uniqueness of a solution for the differential problem, we study its approximation by Rothe's method. We prove a result of stability and another concerning the order of approximation of the solution in dependence of its regularity. The mail tool is a maximal regularity result for solutions to abstract parabolic finite difference schemes. Two model problems to which the results are applicable are illustrated.}},
  author       = {{De Staelen, Rob and Guidetti, Davide}},
  issn         = {{1532-2467}},
  journal      = {{NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION}},
  keywords     = {{Rothe’s method,semigroup theory,Convolution kernel,inverse problem,SEMILINEAR PARABOLIC PROBLEM,CONVOLUTION KERNEL,WAVE-EQUATION,MEMORY,RECONSTRUCTION,IDENTIFICATION,SPACES,SOBOLEV,BESOV,MODEL}},
  language     = {{eng}},
  number       = {{7}},
  pages        = {{850--886}},
  publisher    = {{Taylor & Francis}},
  title        = {{On a finite difference scheme for an inverse integro-differential problem using semigroup theory: a functional analytic approach}},
  url          = {{http://dx.doi.org/10.1080/01630563.2016.1180630}},
  volume       = {{37}},
  year         = {{2016}},
}

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