On a finite difference scheme for an inverse integro-differential problem using semigroup theory: a functional analytic approach
- Author
- Rob De Staelen (UGent) and Davide Guidetti
- Organization
- 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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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-7186074
- 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, vol. 37, no. 7, Taylor & Francis, 2016, pp. 850–86, doi:10.1080/01630563.2016.1180630.
- 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. https://doi.org/10.1080/01630563.2016.1180630
- 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): 850–86. https://doi.org/10.1080/01630563.2016.1180630.
- 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. doi:10.1080/01630563.2016.1180630.
- 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. 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://doi.org/10.1080/01630563.2016.1180630}}, volume = {{37}}, year = {{2016}}, }
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