The behavior of energy E(t) is studied for a class of reaction diffusion equation u t=f(u)+εΔu; here ε > 0. The asymptotic behavior of the energy is of particular interest to indicate singularity formation in the solution in the long run. While for sufficiently large diffusion coefficient ε > 0, decay of energy is expected, small ε or the limiting ε = 0, show some interesting behavior which is related to the singularity formation of solutions in the long run. From the numerical experiments we observe that energy may tend to a non trivial asymptotic, and in some cases it may grow unboundedly. © 2012 American Institute of Physics.

Blow up,Decay,Energy,Reaction diffusion equation

https://doi.org/10.1063/1.4724169