On the Porous Medium Equation with Modified Fourier's Law:Symmetries and Integrability

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The paper considers the general fortn of' the porous Kzledittt'rn Equation ./'(r)uz(y(.r)D(u)(u.)"). f H (u)u., xvhere the probalcility density and fltrx olcey the tnodified Four'ier'slaw and flue drift ternas are not ornitted. The conditions for inxzariance are applied to defermine the ftrnctional forms of the arbitrar3z ftmractions f, .q atnd H xvhich adnait the syrntaaetryreduction transfortnations. XX7e have sttrdied uaaodels dejoending on the ['ttnctional ['orm of' 7)(u):1 - D(u) : u" and 2 - D(u) : e"". A catalogue of syuaanuetry reductiota, to ordinary dif['erentialequation ODB, is given to each systeraa incltrding its integrability.
社団法人日本物理学会の論文
1999-02-15