Representation of the solution of a nonlinear molecular beam epitaxy equation
Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. In this paper, we focus on a specific type of such SPDEs, namely the nonlinear beam e...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2024-12-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241708 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590743874568192 |
|---|---|
| author | Boubaker Smii |
| author_facet | Boubaker Smii |
| author_sort | Boubaker Smii |
| collection | DOAJ |
| description | Stochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. In this paper, we focus on a specific type of such SPDEs, namely the nonlinear beam epitaxy equation driven by Lévy noise. The Feynman graph formalism emerges as a potent tool for analyzing these SPDEs, particularly in computing their correlation functions, which are essential for understanding the moments of the solution. In this context, the solution to the SPDE and its truncated moments can be expressed as a sum over particular Feynman graphs. Each graph is evaluated according to a set of established rules, providing a systematic method to derive the properties of the solution. Moreover, the study delves into the behavior of the truncated moments for large times. Truncated moments, which capture the statistical properties of the system up to a certain order, are crucial for characterizing the long-term behavior and stability of the solution. The paper will conclude with a discussion on potential applications, highlighting the broader implications of this approach in various scientific and engineering contexts. |
| format | Article |
| id | doaj-art-57372e02261649dbbee969d8390edbba |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-57372e02261649dbbee969d8390edbba2025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912360123603010.3934/math.20241708Representation of the solution of a nonlinear molecular beam epitaxy equationBoubaker Smii0King Fahd University of Petroleum and Minerals, Department of Mathematics, Interdisciplinary Research center for Intelligent Secure System, Dhahran 31261, Saudi ArabiaStochastic partial differential equations (SPDEs) driven by Lévy noise are extensively employed across various domains such as physics, finance, and engineering to simulate systems experiencing random fluctuations. In this paper, we focus on a specific type of such SPDEs, namely the nonlinear beam epitaxy equation driven by Lévy noise. The Feynman graph formalism emerges as a potent tool for analyzing these SPDEs, particularly in computing their correlation functions, which are essential for understanding the moments of the solution. In this context, the solution to the SPDE and its truncated moments can be expressed as a sum over particular Feynman graphs. Each graph is evaluated according to a set of established rules, providing a systematic method to derive the properties of the solution. Moreover, the study delves into the behavior of the truncated moments for large times. Truncated moments, which capture the statistical properties of the system up to a certain order, are crucial for characterizing the long-term behavior and stability of the solution. The paper will conclude with a discussion on potential applications, highlighting the broader implications of this approach in various scientific and engineering contexts.https://www.aimspress.com/article/doi/10.3934/math.20241708spdeslévy noisegreen functionsfeynman graphstruncated moments |
| spellingShingle | Boubaker Smii Representation of the solution of a nonlinear molecular beam epitaxy equation AIMS Mathematics spdes lévy noise green functions feynman graphs truncated moments |
| title | Representation of the solution of a nonlinear molecular beam epitaxy equation |
| title_full | Representation of the solution of a nonlinear molecular beam epitaxy equation |
| title_fullStr | Representation of the solution of a nonlinear molecular beam epitaxy equation |
| title_full_unstemmed | Representation of the solution of a nonlinear molecular beam epitaxy equation |
| title_short | Representation of the solution of a nonlinear molecular beam epitaxy equation |
| title_sort | representation of the solution of a nonlinear molecular beam epitaxy equation |
| topic | spdes lévy noise green functions feynman graphs truncated moments |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241708 |
| work_keys_str_mv | AT boubakersmii representationofthesolutionofanonlinearmolecularbeamepitaxyequation |