Building of mathematical models of continuum media on the basis of the invariance principle |
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Authors: | V O Bytev |
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Institution: | (1) Krasnoyarsk State University, 660062 Krasnoyarsk, U.S.S.R. |
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Abstract: | The system of differential equations which describes the motion of continuum media of gas, liquid, Reiner-Rievling-type liquid, etc., is considered.% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqaHbp% GCdaWgaaWcbaGaamiDaaqabaGccqGHRaWkcaqGKbGaaeyAaiaabAha% caqGOaGaeqyWdiNaaeyDaiaabMcacaqG9aGaaeimaiaabUdaaeaacq% aHbpGCcaGGBbGaaeyDamaaBaaaleaacaqG0baabeaakiabgUcaRiaa% cIcacaqG1bGaeyyXICTaey4bIeTaaiykaiaabwhacaGGDbGaeyOeI0% IaamizaiaadMgacaWG2bGaey4dIuTaaiikaiabgEGirlaabwhacaGG% PaGaey4kaSIaey4bIeTaamiCaiaacUdaaeaacaWGWbWaaSbaaSqaai% aadshaaeqaaOGaey4kaSIaaeyDaiabgwSixlabgEGirlaadchacqGH% RaWkcaWGhbGaaeizaiaabMgacaqG2bGaaeiiaiaabwhacqGHRaWkca% WGibGaeqOXdyMaeyypa0JaaGimaiaac6caaaaa!7268!\\begin{gathered} \rho _t + {\text{div(}}\rho {\text{u) = 0;}} \hfill \\ \rho {\text{u}}_{\text{t}} + ({\text{u}} \cdot \nabla ){\text{u}}] - div\prod (\nabla {\text{u}}) + \nabla p; \hfill \\ p_t + {\text{u}} \cdot \nabla p + G{\text{div u}} + H\phi = 0. \hfill \\ \end{gathered} \]Solving the problem of its group classification, we obtained all the state equations which lead to the expansion of the main group assumed by the initial equations under the arbitrary elements , G, H. |
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Keywords: | 73Bxx 22E70 |
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