Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells
In a previous paper a mathematical model was developed for thedynamics of activation and clonal expansion of T cells during theimmune response to a single type of antigen challenge, constructedphenomenologically in the macroscopic framework of a thermodynamictheory of continuum mechanicsfor react...
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AIMS Press
2012-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.59 |
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| author | D. Criaco M. Dolfin L. Restuccia |
| author_facet | D. Criaco M. Dolfin L. Restuccia |
| author_sort | D. Criaco |
| collection | DOAJ |
| description | In a previous paper a mathematical model was developed for thedynamics of activation and clonal expansion of T cells during theimmune response to a single type of antigen challenge, constructedphenomenologically in the macroscopic framework of a thermodynamictheory of continuum mechanicsfor reacting and proliferatingfluid mixtures. The present contribution deals with approximate smooth solutions, called asymptotic waves, of the system of PDEs describing the introduced model, obtained using a suitable perturbative method. In particular, in the one-dimensional case, after deriving the expression of the velocity along the characteristic rays and the equation of the wave front, the transport equation for the first perturbation term of the asymptotic solution is obtained. Finally, it is shown that this transport equation can be reduced to an equation similar to Burgers equation. |
| format | Article |
| id | doaj-art-4cbb6e6a7ef34275991fa25b7505f5b2 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4cbb6e6a7ef34275991fa25b7505f5b22025-01-24T02:25:25ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-11-01101597310.3934/mbe.2013.10.59Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cellsD. Criaco0M. Dolfin1L. Restuccia2Department of Mathematics and Informatics, University of Messina, Viale F. Stagno d'Alcontres n.31, 98166 MessinaDepartment of Mathematics and Informatics, University of Messina, Viale F. Stagno d'Alcontres n.31, 98166 MessinaDepartment of Mathematics and Informatics, University of Messina, Viale F. Stagno d'Alcontres n.31, 98166 MessinaIn a previous paper a mathematical model was developed for thedynamics of activation and clonal expansion of T cells during theimmune response to a single type of antigen challenge, constructedphenomenologically in the macroscopic framework of a thermodynamictheory of continuum mechanicsfor reacting and proliferatingfluid mixtures. The present contribution deals with approximate smooth solutions, called asymptotic waves, of the system of PDEs describing the introduced model, obtained using a suitable perturbative method. In particular, in the one-dimensional case, after deriving the expression of the velocity along the characteristic rays and the equation of the wave front, the transport equation for the first perturbation term of the asymptotic solution is obtained. Finally, it is shown that this transport equation can be reduced to an equation similar to Burgers equation.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.59proliferative eventsapproximate smooth solutionsthermodynamic theory of fluid mixturesperturbative methods. |
| spellingShingle | D. Criaco M. Dolfin L. Restuccia Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells Mathematical Biosciences and Engineering proliferative events approximate smooth solutions thermodynamic theory of fluid mixtures perturbative methods. |
| title | Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells |
| title_full | Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells |
| title_fullStr | Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells |
| title_full_unstemmed | Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells |
| title_short | Approximate smooth solutions of a mathematical model for the activation and clonal expansion of T cells |
| title_sort | approximate smooth solutions of a mathematical model for the activation and clonal expansion of t cells |
| topic | proliferative events approximate smooth solutions thermodynamic theory of fluid mixtures perturbative methods. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.59 |
| work_keys_str_mv | AT dcriaco approximatesmoothsolutionsofamathematicalmodelfortheactivationandclonalexpansionoftcells AT mdolfin approximatesmoothsolutionsofamathematicalmodelfortheactivationandclonalexpansionoftcells AT lrestuccia approximatesmoothsolutionsofamathematicalmodelfortheactivationandclonalexpansionoftcells |