Semenov E. I.
Multidimensional exact solutions to a quasilinear parabolic
equation with anisotropic heat conductivity
We prove invariance of a quasilinear parabolic equation with anisotropic
heat conductivity in the three-dimensional coordinate space under some
equivalence transformations and present some explicit formulas for these
transformations. We consider nontrivial reductions of the equation to
similar equations of less spatial dimension. Using these results, we
construct new exact multidimensional solutions to the equation which
depend on arbitrary harmonic functions.