Asymptotically Self-Similar Solution for the Convection-Diffusion Equation

Xue Yu; Qiu Sheng Zhang

doi:10.4028/www.scientific.net/AMM.623.97

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 623Asymptotically Self-Similar Solution for the...

Asymptotically Self-Similar Solution for the Convection-Diffusion Equation

Abstract:

We study the Cauchy problem for the convection-diffusion equation, which describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to diffusion and convection processes. For, we show the continuous dependence upon the initial data. Moreover, asymptotically self–similar global solutions are investigated with nonhomogeneous initial date.

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Periodical:

Applied Mechanics and Materials (Volume 623)

Pages:

97-100

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.623.97

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Online since:

August 2014

Authors:

Xue Yu*, Qiu Sheng Zhang

Keywords:

Asymptotically Self–Similar Solution, Cauchy Problem, Convection-Diffusion Equation

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References

[1] M. Kardar, G. parisi, Y.C. Zhang, Dynamic scaling of growing interfaces, Physical Review Letters, 56(1986) 889-892.

DOI: 10.1103/physrevlett.56.889

Google Scholar

[2] M. Assila, Stability of solutions to the Burgers equation, Asymptotic Analysis, 30(2002) 131-160.

Google Scholar

[3] E. Zahrouni, On the role of the Besov spaces for the solutions of the generalized burgers equation in homogeneous Sobolev spaces, Nonlinear Analysis: Theory, Methods & Applications, 54(2003) 39-62.

DOI: 10.1016/s0362-546x(03)00035-x

Google Scholar

[4] C. Miao, B. Zhang, Besov spaces and self-similar solutions for nonlinear evolution equations, Partial Diff. Eqs., 19(2006)26-47.

Google Scholar

[5] F. Ribaud, A Youssif, Global solutions and self-similar solutions of semilinear wave equation, Math. Z., 239(2002) 231-262.

DOI: 10.1007/s002090100293

Google Scholar

[6] S. Snoussi, S. Tayachi, and F.B. Weissler, Asymptotically self-similar global solutions of a general semilinear heat equation, Math. Ann. 321(2001)131-155.

DOI: 10.1007/pl00004498

Google Scholar

[7] Q. Zhang, P. Shi, Global solutions and self-similar solutions of semilinear parabolic equations with nonlinear gradient terms, Nonlinear Analysis: Theory, Methods & Applications, 72(2010)2744-2752.

DOI: 10.1016/j.na.2009.11.020

Google Scholar