Nonlinear Diffusion Equations and Their Equilibrium States II: Proceedings of a Microprogram held August 25–September 12, 1986
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer US
1988
|
| Series: | Mathematical Sciences Research Institute Publications
13 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution |
| Physical Description: | 1 Online-Ressource (XIII, 365p. 34 illus) |
| ISBN: | 9781461396086 9781461396109 |
| ISSN: | 0940-4740 |
| DOI: | 10.1007/978-1-4613-9608-6 |
Staff View
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| 500 | |a In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution | ||
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Record in the Search Index
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| discipline | Mathematik |
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| id | DE-604.BV042420812 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461396086 9781461396109 |
| issn | 0940-4740 |
| language | English |
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| publishDate | 1988 |
| publishDateSearch | 1988 |
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| publisher | Springer US |
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| series2 | Mathematical Sciences Research Institute Publications |
| spelling | Ni, W.-M. Verfasser aut Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 edited by W.-M. Ni, L. A. Peletier, James Serrin New York, NY Springer US 1988 1 Online-Ressource (XIII, 365p. 34 illus) txt rdacontent c rdamedia cr rdacarrier Mathematical Sciences Research Institute Publications 13 0940-4740 In recent years considerable interest has been focused on nonlinear diffu sion problems, the archetypical equation for these being Ut = ~U + f(u). Here ~ denotes the n-dimensional Laplacian, the solution u = u(x, t) is defined over some space-time domain of the form n x [O,T], and f(u) is a given real function whose form is determined by various physical and mathematical applications. These applications have become more varied and widespread as problem after problem has been shown to lead to an equation of this type or to its time-independent counterpart, the elliptic equation of equilibrium ~u+f(u)=O. Particular cases arise, for example, in population genetics, the physics of nu clear stability, phase transitions between liquids and gases, flows in porous media, the Lend-Emden equation of astrophysics, various simplified com bustion models, and in determining metrics which realize given scalar or Gaussian curvatures. In the latter direction, for example, the problem of finding conformal metrics with prescribed curvature leads to a ground state problem involving critical exponents. Thus not only analysts, but geome ters as well, can find common ground in the present work. The corresponding mathematical problem is to determine how the struc ture of the nonlinear function f(u) influences the behavior of the solution Mathematics Global analysis (Mathematics) Analysis Mathematik Peletier, L. A. Sonstige oth Serrin, James Sonstige oth https://doi.org/10.1007/978-1-4613-9608-6 Verlag Volltext |
| spellingShingle | Ni, W.-M Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 Mathematics Global analysis (Mathematics) Analysis Mathematik |
| title | Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 |
| title_auth | Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 |
| title_exact_search | Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 |
| title_full | Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 edited by W.-M. Ni, L. A. Peletier, James Serrin |
| title_fullStr | Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 edited by W.-M. Ni, L. A. Peletier, James Serrin |
| title_full_unstemmed | Nonlinear Diffusion Equations and Their Equilibrium States II Proceedings of a Microprogram held August 25–September 12, 1986 edited by W.-M. Ni, L. A. Peletier, James Serrin |
| title_short | Nonlinear Diffusion Equations and Their Equilibrium States II |
| title_sort | nonlinear diffusion equations and their equilibrium states ii proceedings of a microprogram held august 25 september 12 1986 |
| title_sub | Proceedings of a Microprogram held August 25–September 12, 1986 |
| topic | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Analysis Mathematik |
| url | https://doi.org/10.1007/978-1-4613-9608-6 |
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