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Reduction of Balance Laws in (3+1)-Dimensions to Autonomous Conservation Laws by Means of Equivalence Transformations

Abstract

A class of partial differential equations (a conservation law and four balance laws), with four independent variables and involving sixteen arbitrary continuously differentiable functions, is considered in the framework of equivalence transformations. These are point transformations of differential equations involving arbitrary elements and live in an augmented space of independent, dependent and additional variables representing values taken by the arbitrary elements. Projecting the admitted infinitesimal equivalence transformations into the space of independent and dependent variables, we determine some finite transformations mapping the system of balance laws to an equivalent one with the same differential structure but involving different arbitrary elements; in particular, the target system we want to recover is an autonomous system of conservation laws. An application to a physical problem is considered.

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Correspondence to M. P. Speciale.

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Gorgone, M., Oliveri, F. & Speciale, M.P. Reduction of Balance Laws in (3+1)-Dimensions to Autonomous Conservation Laws by Means of Equivalence Transformations. Acta Appl Math 132, 333–345 (2014). https://doi.org/10.1007/s10440-014-9929-5

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Keywords

  • Systems of balance laws
  • Equivalence transformations
  • Derivation of autonomous and homogeneous conservation laws