M. Euler et al., ON THE CONSTRUCTION OF APPROXIMATE SOLUTIONS FOR A MULTIDIMENSIONAL NONLINEAR HEAT-EQUATION, Journal of physics. A, mathematical and general, 27(6), 1994, pp. 2083-2092
We study three methods, based on continuous symmetries, to find approx
imate solutions for the multidimensional nonlinear heat equation parti
al derivate u/partial derivate x0 + DELTAu = au(n) + epsilonf(u), wher
e a and n are arbitrary real constants, f is a smooth function, and 0
< epsilon much less than 1.