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

Abstract

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.