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Solutions with Dead Cores for a Parabolic P-Laplacian Equation
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Advances in Pure Mathematics·Volume 01 (2011)·Pages 280–283·Published 21 September 2011·DOI10.4236/apm.2011.15050
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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.
KeywordsParabolic P-Laplacian EquationSteady StateDead CoreDecay Estimates
- C. Bandle and S. Vernier-Piro, “Estimates for Solutions of Quasilinear Problems with Dead Cores,” Zeitschrift für Ange-wandte Mathematik und Physik, Vol. 54, No. 5, 2003, pp. 815-821.
- 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
- 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.
- 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