Journal article 852 views 138 downloads
Heterogeneous stochastic scalar conservation laws with non-homogeneous Dirichlet boundary conditions
Guangying Lv,
Jiang-lun Wu 
Journal of Hyperbolic Differential Equations, Volume: 15, Issue: 02, Pages: 291 - 328
Swansea University Author:
Jiang-lun Wu
DOI (Published version): 10.1142/S021989161850011X
Abstract
We introduce a notion of stochastic entropy solutions for heterogeneous scalar conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition. Using the concept of measure-valued solutions and Kruzhkov's semi-entropy formulations, we show the existence a...
| Published in: | Journal of Hyperbolic Differential Equations |
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| ISBN: | 1793-6993 |
| ISSN: | 0219-8916 1793-6993 |
| Published: |
Singapore
World Scientific
2018
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| Online Access: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa38288 |
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| Abstract: |
We introduce a notion of stochastic entropy solutions for heterogeneous scalar conservation laws with multiplicative noise on a bounded domain with non-homogeneous boundary condition. Using the concept of measure-valued solutions and Kruzhkov's semi-entropy formulations, we show the existence and uniqueness of stochastic entropy solutions. Moreover, we establish an explicit estimate for the continuous dependence of stochastic entropy solutions on the flux function and the random source function. |
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| Keywords: |
Scalar conservation law; entropy solutions; It\^{o}'s formula. |
| College: |
Faculty of Science and Engineering |
| Issue: |
02 |
| Start Page: |
291 |
| End Page: |
328 |