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The Self–similar Solution to Some Nonlinear Integro–differential Equations Corresponding to Fractional Order Time Derivative

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Abstract

In this paper we study the self–similar solution to a class of nonlinear integro–differential equations which correspond to fractional order time derivative and interpolate nonlinear heat and wave equation. Using the space–time estimates which were established by Hirata and Miao in [11] we prove the global existence of self–similar solution of Cauchy problem for the nonlinear integro-differential equation in \( C_{*} ([0,\infty );\dot{B}^{{s_{p} }}_{{p,\infty }} (\mathbb{R}^{n} )). \)

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, 8009, Bei**g 100088, P. R. China

    Chang **ng Miao

  2. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, P. R. China

    Han Yang

Authors
  1. Chang **ng Miao
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  2. Han Yang
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Correspondence to Chang **ng Miao.

Additional information

The first author is supported by NSF of China, Special Funds for Major State Basic Research Projects of China and NSF of Chinese Academy of Engineering Physics

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Miao, C.X., Yang, H. The Self–similar Solution to Some Nonlinear Integro–differential Equations Corresponding to Fractional Order Time Derivative. Acta Math Sinica 21, 1337–1350 (2005). https://doi.org/10.1007/s10114-005-0546-0

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  • DOI: https://doi.org/10.1007/s10114-005-0546-0

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