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Title: Blow-up solutions of degenerate parabolic problems
Authors: P. Sawangtong
W. Jumpen
King Mongkut's University of Technology North Bangkok
Mahidol University
Center of Excellence in Mathematics
Keywords: Mathematics
Issue Date: 1-Sep-2010
Citation: WSEAS Transactions on Mathematics. Vol.9, No.9 (2010), 723-733
Abstract: In this article, we study the degenerate parabolic problem, x qut-(x βu x) x = x qf(u), satisfying the Dirichlet boundary condition and a nonnegative initial condition where q and β are given constants and f is a suitable function. We show that under certain conditions the degenerate parabolic problem has a blow-up solution and the blow-up set of such a blow-up solution is the whole domain of x. Furthermore, we give the sufficient condition to blow-up in finite time. Finally, we generalize the degenerate parabolic problem into the general form, k(x)u t-(p(x)u x) x =k(x)f(u). Under appropriate assumptions on functions k, p and f, we still obtain the same results as the previous problem.
ISSN: 11092769
Appears in Collections:Scopus 2006-2010

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