Determination of a time-dependent convolution kernel in a non-linear hyperbolic equation
- Author
- Marian Slodicka (UGent) and Lukas Seliga (UGent)
- Organization
- Abstract
- A nonlinear wave equation with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional (space) integral measurement. The global in time existence, uniqueness as well as the regularity of a solution is addressed. A new numerical algorithm based on Rothe's method is designed and error estimates are derived.
- Keywords
- SEMILINEAR PARABOLIC PROBLEM, INTEGRODIFFERENTIAL EQUATION, INTEGRAL OVERDETERMINATION, INVERSE PROBLEM, MEMORY KERNELS, RECONSTRUCTION, REGULARIZATION, IDENTIFICATION, Wave equation, convolution kernel, reconstruction, error estimate, time discretization
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-7897989
- MLA
- Slodicka, Marian, and Lukas Seliga. “Determination of a Time-Dependent Convolution Kernel in a Non-Linear Hyperbolic Equation.” INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, vol. 24, no. 6, TAYLOR & FRANCIS LTD, 2016, pp. 1011–29, doi:10.1080/17415977.2015.1101762.
- APA
- Slodicka, M., & Seliga, L. (2016). Determination of a time-dependent convolution kernel in a non-linear hyperbolic equation. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, 24(6), 1011–1029. https://doi.org/10.1080/17415977.2015.1101762
- Chicago author-date
- Slodicka, Marian, and Lukas Seliga. 2016. “Determination of a Time-Dependent Convolution Kernel in a Non-Linear Hyperbolic Equation.” INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 24 (6): 1011–29. https://doi.org/10.1080/17415977.2015.1101762.
- Chicago author-date (all authors)
- Slodicka, Marian, and Lukas Seliga. 2016. “Determination of a Time-Dependent Convolution Kernel in a Non-Linear Hyperbolic Equation.” INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 24 (6): 1011–1029. doi:10.1080/17415977.2015.1101762.
- Vancouver
- 1.Slodicka M, Seliga L. Determination of a time-dependent convolution kernel in a non-linear hyperbolic equation. INVERSE PROBLEMS IN SCIENCE AND ENGINEERING. 2016;24(6):1011–29.
- IEEE
- [1]M. Slodicka and L. Seliga, “Determination of a time-dependent convolution kernel in a non-linear hyperbolic equation,” INVERSE PROBLEMS IN SCIENCE AND ENGINEERING, vol. 24, no. 6, pp. 1011–1029, 2016.
@article{7897989,
abstract = {{A nonlinear wave equation with an unknown time-convolution kernel is considered. The missing kernel is recovered from an additional (space) integral measurement. The global in time existence, uniqueness as well as the regularity of a solution is addressed. A new numerical algorithm based on Rothe's method is designed and error estimates are derived.}},
author = {{Slodicka, Marian and Seliga, Lukas}},
issn = {{1741-5977}},
journal = {{INVERSE PROBLEMS IN SCIENCE AND ENGINEERING}},
keywords = {{SEMILINEAR PARABOLIC PROBLEM,INTEGRODIFFERENTIAL EQUATION,INTEGRAL OVERDETERMINATION,INVERSE PROBLEM,MEMORY KERNELS,RECONSTRUCTION,REGULARIZATION,IDENTIFICATION,Wave equation,convolution kernel,reconstruction,error estimate,time discretization}},
language = {{eng}},
number = {{6}},
pages = {{1011--1029}},
publisher = {{TAYLOR & FRANCIS LTD}},
title = {{Determination of a time-dependent convolution kernel in a non-linear hyperbolic equation}},
url = {{http://doi.org/10.1080/17415977.2015.1101762}},
volume = {{24}},
year = {{2016}},
}
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