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Solutions with Dead Cores for a Parabolic P-Laplacian Equation

DOI: 10.4236/apm.2011.15050, PP. 280-283

Keywords: Parabolic P-Laplacian Equation, Steady State, Dead Core, Decay Estimates

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Abstract:

We study the solutions with dead cores and the decay estimates for a parabolic p-Laplacian equation with absorption by sub- and supersolution method. Special attention is given to the case where the solution of the steady-state problem vanishes in an interior region.

References

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[2]  X. F. Chen, Y. W. Qi and M. X. Wang, “Long Time Behavior of Solutions to P-Laplacian Equation with Ab-sorption,” SIAM Journal on Mathematical Analysis, Vol. 35, No. 1, 2003, pp. 123-134. doi:10.1137/S0036141002407727
[3]  X. F. Chen, Y. W. Qi and M. X. Wang, “Singular Solutions of Parabolic P-Lapacian with Absorption,” Transactions of the American Mathemarical Society, Vol. 359 2007, pp. 5653-5668.
[4]  C. Bandle, T.Nanbu, I. Stakgold, “Porous Medium Equation with Absorp-tion,” SIAM Journal on Mathematical Analysis, Vol. 29, 1998, pp. 1268-1278. doi:10.1137/S0036141096311423

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