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Blow-Up Phenomena of a Cancer Invasion Model with Nonlinear Diffusion and Haptotaxis Term

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Abstract

In this paper, we consider a nonlinear cancer invasion mathematical model with proliferation, growth and haptotaxis effects. We obtain lower bounds for the finite-time blow-up of solutions of the considered system with nonlinear diffusion operator when blow-up occurs. We have assumed both the Dirichlet and Neumann boundary conditions in \({\mathbb {R}}^n, n\ge 2\) to attain the desire result.

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Acknowledgements

The work of the second author is supported by the University Research Fellowship of Periyar University and the work fourth author is supported by the Special Assistance Programme (SAP) of the University Grants Commission (F-510/7/DRSI/2016 (SAP-I)) and Fund for Improvement of S&T Infrastructure (FIST) of the Department of Science and Technology (SR/FST/MSI-115/2016).

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Authors and Affiliations

  1. Department of Applied Sciences, National Institute of Technology, Goa, 403 401, India

    L. Shangerganesh

  2. Department of Mathematics, Periyar University, Salem, 636 011, India

    G. Sathishkumar & S. Karthikeyan

  3. Department of Mathematics, Faculty of Sciences, Razi University, 67149, Kermanshah, Iran

    N. Nyamoradi

Authors
  1. L. Shangerganesh
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  2. G. Sathishkumar
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  3. N. Nyamoradi
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  4. S. Karthikeyan
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Corresponding author

Correspondence to N. Nyamoradi.

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Communicated by Yong Zhou.

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Shangerganesh, L., Sathishkumar, G., Nyamoradi, N. et al. Blow-Up Phenomena of a Cancer Invasion Model with Nonlinear Diffusion and Haptotaxis Term. Bull. Malays. Math. Sci. Soc. 44, 1215–1231 (2021). https://doi.org/10.1007/s40840-020-00996-7

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  • DOI: https://doi.org/10.1007/s40840-020-00996-7

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