Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1984
|
| Schriftenreihe: | Applied Mathematical Sciences
53 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm |
| Beschreibung: | 1 Online-Ressource (172p) |
| ISBN: | 9781461211167 9780387960371 |
| ISSN: | 0066-5452 |
| DOI: | 10.1007/978-1-4612-1116-7 |
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Datensatz im Suchindex
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| any_adam_object | |
| author | Majda, A. |
| author_facet | Majda, A. |
| author_role | aut |
| author_sort | Majda, A. |
| author_variant | a m am |
| building | Verbundindex |
| bvnumber | BV042419752 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
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| dewey-full | 530.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.1 |
| dewey-search | 530.1 |
| dewey-sort | 3530.1 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1116-7 |
| format | Electronic eBook |
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| issn | 0066-5452 |
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| spelling | Majda, A. Verfasser aut Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables by A. Majda New York, NY Springer New York 1984 1 Online-Ressource (172p) txt rdacontent c rdamedia cr rdacarrier Applied Mathematical Sciences 53 0066-5452 Conservation laws arise from the modeling of physical processes through the following three steps: 1) The appropriate physical balance laws are derived for m-phy- t cal quantities, ul""'~ with u = (ul' ... ,u ) and u(x,t) defined m for x = (xl""'~) E RN (N = 1,2, or 3), t > 0 and with the values m u(x,t) lying in an open subset, G, of R , the state space. The state space G arises because physical quantities such as the density or total energy should always be positive; thus the values of u are often con strained to an open set G. 2) The flux functions appearing in these balance laws are idealized through prescribed nonlinear functions, F.(u), mapping G into J j = 1, ..• ,N while source terms are defined by S(u,x,t) with S a given smooth function of these arguments with values in Rm. In parti- lar, the detailed microscopic effects of diffusion and dissipation are ignored. 3) A generalized version of the principle of virtual work is applied (see Antman [1]). The formal result of applying the three steps (1)-(3) is that the m physical quantities u define a weak solution of an m x m system of conservation laws, o I + N(Wt'u + r W ·F.(u) + W·S(u,x,t))dxdt (1.1) R xR j=l Xj J for all W E C~(RN x R+), W(x,t) E Rm Physics Theoretical, Mathematical and Computational Physics Gasdynamik (DE-588)4019339-1 gnd rswk-swf Kompressible Strömung (DE-588)4032018-2 gnd rswk-swf Kompressibilität (DE-588)4199865-0 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 gnd rswk-swf Erhaltungssatz (DE-588)4131214-4 gnd rswk-swf Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Hydrodynamik (DE-588)4026302-2 s Kompressibilität (DE-588)4199865-0 s Mathematische Methode (DE-588)4155620-3 s 1\p DE-604 Kompressible Strömung (DE-588)4032018-2 s Erhaltungssatz (DE-588)4131214-4 s Physik (DE-588)4045956-1 s 2\p DE-604 Hyperbolisches System (DE-588)4191897-6 s Strömungsmechanik (DE-588)4077970-1 s 3\p DE-604 Gasdynamik (DE-588)4019339-1 s 4\p DE-604 https://doi.org/10.1007/978-1-4612-1116-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Majda, A. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables Physics Theoretical, Mathematical and Computational Physics Gasdynamik (DE-588)4019339-1 gnd Kompressible Strömung (DE-588)4032018-2 gnd Kompressibilität (DE-588)4199865-0 gnd Hydrodynamik (DE-588)4026302-2 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolisches System (DE-588)4191897-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| subject_GND | (DE-588)4019339-1 (DE-588)4032018-2 (DE-588)4199865-0 (DE-588)4026302-2 (DE-588)4131214-4 (DE-588)4191897-6 (DE-588)4077970-1 (DE-588)4155620-3 (DE-588)4045956-1 |
| title | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables |
| title_auth | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables |
| title_exact_search | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables |
| title_full | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables by A. Majda |
| title_fullStr | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables by A. Majda |
| title_full_unstemmed | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables by A. Majda |
| title_short | Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables |
| title_sort | compressible fluid flow and systems of conservation laws in several space variables |
| topic | Physics Theoretical, Mathematical and Computational Physics Gasdynamik (DE-588)4019339-1 gnd Kompressible Strömung (DE-588)4032018-2 gnd Kompressibilität (DE-588)4199865-0 gnd Hydrodynamik (DE-588)4026302-2 gnd Erhaltungssatz (DE-588)4131214-4 gnd Hyperbolisches System (DE-588)4191897-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Physik (DE-588)4045956-1 gnd |
| topic_facet | Physics Theoretical, Mathematical and Computational Physics Gasdynamik Kompressible Strömung Kompressibilität Hydrodynamik Erhaltungssatz Hyperbolisches System Strömungsmechanik Mathematische Methode Physik |
| url | https://doi.org/10.1007/978-1-4612-1116-7 |
| work_keys_str_mv | AT majdaa compressiblefluidflowandsystemsofconservationlawsinseveralspacevariables |