Extension of relations between local values of intensive properties and corresponding fluxes to some nonlinear processes

  • V Novozhilov
  • Vladimir Kulish


Integral identities, representing relations between unknown field (e.g. temperature or velocity)and its gradient, are known for a number of linear equations of mathematical physics. In the
present paper, similar relations are derived for non-linear PDEs. Two specific examples are considered:(1) the Burgers equation, and (2) the Frank-Kamenetskii equation, arising in combustion theory.It is shown that integral forms of relations for non-linear PDEs exhibit important differences from the known linear cases. Validation and potential applications of obtained relations are also discussed.