Geometry of conservation laws for a class of parabolic PDE's, II: Normal forms for equations with conservation laws

• J.N. Clelland ^[1]
  1. [1] Institute for Advanced Study

     Institute for Advanced Study

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 3, Nº. 4, 1997, págs. 497-515
• Idioma: inglés
• DOI: 10.1007/s000290050018
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• Resumen

  • We consider conservation laws for second-order parabolic partial differential equations for one function of three independent variables. An explicit normal form is given for such equations having a nontrivial conservation law. It is shown that any such equation whose space of conservation laws has dimension at least four is locally contact equivalent to a quasi-linear equation. Examples are given of nonlinear equations that have an infinite-dimensional space of conservation laws parameterized (in the sense of Cartan-Kähler) by two arbitrary functions of one variable. Furthermore, it is shown that any equation whose space of conservation laws is larger than this is locally contact equivalent to a linear equation.