The local analytic solution to some nonlinear diffusion-reaction problems

Authors:
Gabriella Bognár;Erika Rozgonyi
Affiliations:
Department of Analysis, University of Miskolc, Hungary;Department of Analysis, University of Miskolc, Hungary
Venue:
WSEAS Transactions on Mathematics
Year:
2008

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Abstract

The positive radially symmetric solutions to the nonlinear problem div(|∇u|p-2∇u)+f(u)=0 in BR={x∈Rn: |x|R}, 1pn, with f(u) = uγ + uδ for u ≥ 0 are considered. We examine the existence of local solutions and give a method for the determination of power series solutions. The comparison of the local analytic and entire solutions is given for some special values of parameters p, n, γ and δ.