Universal self-similarity of porous media equation with absorption: the critical exponent case |
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Authors: | Yuanwei Qi Xudong Liu |
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Institution: | a Department of Mathematics, UCF, Orlando, FL 32816, USA b Department of Mathematics, UCSB, Santa Barbara, CA 93106, USA |
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Abstract: | In this paper we study the large time behavior of non-negative solutions to the Cauchy problem of ut=Δum−uq in RN×(0,∞), where m>1 and q=qc≡m+2/N is a critical exponent. For non-negative initial value u(x,0)=u0(x)∈L1(RN), we show that the solution converges, if u0(x)(1+|x|)k is bounded for some k>N, to a unique fundamental solution of ut=Δum, independent of the initial value, with additional logarithmic anomalous decay exponent in time as t→∞. |
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Keywords: | 35K65 35K15 |
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