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Nonlinear Evolution Equations with Strong Dissipation and Proliferation

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Current Trends in Analysis and Its Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

We investigate the global existence in time and asymptotic profile of the solution of some nonlinear evolution equations with strong dissipation and proliferation arising in mathematical biology. We apply our result to mathematical models of tumour angiogenesis and invasion with proliferation of tumour cells.

This work was supported in part by the Grants-in-Aid for Scientific Research (C) 16540176, 19540200, 22540208 and 25400148 from Japan Society for the Promotion of Science.

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Acknowledgement

The authors thank the referee for fruitful suggestions, especially for suggesting the better terms and sentences.

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Authors and Affiliations

  1. Fujita Health University, Toyoake, Aichi, 470-1192, Japan

    Akisato Kubo & Hiroki Hoshino

Authors
  1. Akisato Kubo
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  2. Hiroki Hoshino
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Corresponding author

Correspondence to Akisato Kubo .

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Editors and Affiliations

  1. Dept. of Computer Sc. & Comp. Methods, Pedagogical University, KrakĂłw, Poland

    Vladimir V. Mityushev

  2. Imperial College London, London, United Kingdom

    Michael V. Ruzhansky

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Kubo, A., Hoshino, H. (2015). Nonlinear Evolution Equations with Strong Dissipation and Proliferation. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_28

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