Abstract
A reduction aproach is developed for determining exact solutions of anonlinear second order parabolic PDE. The method in point makes acomplementary use of the leading ideas of the theory of quasilinearhyperbolic systems of first order endowed by differential constraintsand of the techniques providing multiple wave-like solutions ofnonlinear PDEs. The searched solutions exhibit a inherent wave featuresand they are obtained by solving a consistent overdetermined system ofPDEs. Remarkably, in the process it is possible to define nonlinearmodel equations which allow special classes of initial or boundary valueproblems to be solved in a closed form. Within the present reductionapproach exact solutions and model material response functions areobtained for an equation of widespread application in many fields ofinterest.
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