TY - JOUR
T1 - Asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case
AU - Ogawa, Takayoshi
AU - Suguro, Takeshi
N1 - Funding Information:
The authors would like to thank the referee for helpful suggestions and comments. The work of the first author is partially supported by JSPS Grant-in-Aid for Scientific Research S # 19H05597 , Challenging Research (Pioneering) # 20K20284 , and Grant-in-Aid for Scientific Research B # 18H01131 . The second author is supported by JSPS Grant-in-Aid for JSPS Fellows # 19J20763 . The authors are grateful to Professor Marek Fila and Professor Masashi Misawa for information on the Zel'dovich–Kompaneetz–Barenblatt function.
Publisher Copyright:
© 2021 The Authors
PY - 2022/1/15
Y1 - 2022/1/15
N2 - We consider asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case. In the degenerate drift-diffusion equation, it is known that large time behavior of solutions converges to the Zel'dovich–Kompaneetz–Barenblatt (ZKB) function. For a fast-diffusion case, we show that the asymptotic profile for a solution is the generalized ZKB function such as the Talenti function. We use the entropy dissipation method combining the logarithmic Sobolev and the Shannon inequalities for the Rényi entropy that is known as an extension of the Boltzmann–Shannon entropy.
AB - We consider asymptotic behavior of a solution to the drift-diffusion equation for a fast-diffusion case. In the degenerate drift-diffusion equation, it is known that large time behavior of solutions converges to the Zel'dovich–Kompaneetz–Barenblatt (ZKB) function. For a fast-diffusion case, we show that the asymptotic profile for a solution is the generalized ZKB function such as the Talenti function. We use the entropy dissipation method combining the logarithmic Sobolev and the Shannon inequalities for the Rényi entropy that is known as an extension of the Boltzmann–Shannon entropy.
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U2 - 10.1016/j.jde.2021.10.032
DO - 10.1016/j.jde.2021.10.032
M3 - Article
AN - SCOPUS:85118554732
SN - 0022-0396
VL - 307
SP - 114
EP - 136
JO - Journal of Differential Equations
JF - Journal of Differential Equations
ER -