On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain
This paper is devoted to the mathematical analysis of a spatially homogeneous thermostatted kinetic theory framework with an unbounded activity domain. The framework consists of a partial integro-differential equation with quadratic nonlinearity where the domain of the activity variable is the whole...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-04-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/9/1407 |
| _version_ | 1797503851768578048 |
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| author | Carlo Bianca Marco Menale |
| author_facet | Carlo Bianca Marco Menale |
| author_sort | Carlo Bianca |
| collection | DOAJ |
| description | This paper is devoted to the mathematical analysis of a spatially homogeneous thermostatted kinetic theory framework with an unbounded activity domain. The framework consists of a partial integro-differential equation with quadratic nonlinearity where the domain of the activity variable is the whole real line. Specifically the mathematical analysis refers firstly to the existence and uniqueness of the solution for the related initial boundary value problem; Secondly the investigations are addressed to the existence of a class of self-similar solutions by employing the Fourier transform method. In particular the main result is obtained for a nonconstant interaction rate and a nonconstant force field. Conclusions and perspectives are discussed in the last section of the paper. |
| first_indexed | 2024-03-10T03:56:17Z |
| format | Article |
| id | doaj.art-16e007b012204d439b66894470313324 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:56:17Z |
| publishDate | 2022-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-16e007b012204d439b668944703133242023-11-23T08:43:50ZengMDPI AGMathematics2227-73902022-04-01109140710.3390/math10091407On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity DomainCarlo Bianca0Marco Menale1Laboratoire Quartz EA 7393, École Supérieure d’Ingénieurs en Génie Électrique, Productique et Management Industriel, 13 Boulevard de l’Hautil, 95092 Cergy Pontoise, FranceDipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli", Viale Lincoln 5, I-81100 Caserta, ItalyThis paper is devoted to the mathematical analysis of a spatially homogeneous thermostatted kinetic theory framework with an unbounded activity domain. The framework consists of a partial integro-differential equation with quadratic nonlinearity where the domain of the activity variable is the whole real line. Specifically the mathematical analysis refers firstly to the existence and uniqueness of the solution for the related initial boundary value problem; Secondly the investigations are addressed to the existence of a class of self-similar solutions by employing the Fourier transform method. In particular the main result is obtained for a nonconstant interaction rate and a nonconstant force field. Conclusions and perspectives are discussed in the last section of the paper.https://www.mdpi.com/2227-7390/10/9/1407kinetic theorycomplex systemnonlinearityFourier transformIBV problem |
| spellingShingle | Carlo Bianca Marco Menale On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain Mathematics kinetic theory complex system nonlinearity Fourier transform IBV problem |
| title | On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain |
| title_full | On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain |
| title_fullStr | On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain |
| title_full_unstemmed | On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain |
| title_short | On the Existence of Self-Similar Solutions in the Thermostatted Kinetic Theory with Unbounded Activity Domain |
| title_sort | on the existence of self similar solutions in the thermostatted kinetic theory with unbounded activity domain |
| topic | kinetic theory complex system nonlinearity Fourier transform IBV problem |
| url | https://www.mdpi.com/2227-7390/10/9/1407 |
| work_keys_str_mv | AT carlobianca ontheexistenceofselfsimilarsolutionsinthethermostattedkinetictheorywithunboundedactivitydomain AT marcomenale ontheexistenceofselfsimilarsolutionsinthethermostattedkinetictheorywithunboundedactivitydomain |