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On Lipschitz solutions for some forward–backward parabolic equations. II: the case against Fourier

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Abstract

As a sequel to the paper Kim and Yan (Ann Inst H Poincaré Anal Non Linéaire. doi:10.1016/j.anihpc.2017.03.001, 2017), we study the existence and properties of Lipschitz solutions to the initial-boundary value problem of some forward–backward diffusion equations with diffusion fluxes violating Fourier’s inequality.

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Acknowledgements

The authors would like thank the anonymous referee for many helpful suggestions that greatly improve the presentation of the paper. The first author was partially supported by China Overseas Postdoctoral Recruitment Program.

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Authors and Affiliations

  1. Institute for Mathematical Sciences, Renmin University of China, Beijing, 100872, People’s Republic of China

    Seonghak Kim

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    Baisheng Yan

Authors
  1. Seonghak Kim
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  2. Baisheng Yan
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Correspondence to Seonghak Kim.

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Communicated by J. Ball.

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Kim, S., Yan, B. On Lipschitz solutions for some forward–backward parabolic equations. II: the case against Fourier. Calc. Var. 56, 67 (2017). https://doi.org/10.1007/s00526-017-1155-3

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  • DOI: https://doi.org/10.1007/s00526-017-1155-3

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