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Volume 24, Issue 1
Nonlinear Hyperbolic-parabolic System Modeling Some Biological Phenomena

Shaohua Wu & Hua Chen

DOI: 10.4208/jpde.v24.n1.1

J. Part. Diff. Eq., 24 (2011), pp. 1-14.

Published online: 2011-02

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  • Abstract

In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N=1, the global existence of the weak solution will be established by the bootstrap argument.

  • Keywords

Hyperbolic-parabolic system chemosensitive movement external signal global existence

  • AMS Subject Headings

35A07 35K50 35M10 35L10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-24-1, author = {Shaohua Wu and Hua Chen}, title = {Nonlinear Hyperbolic-parabolic System Modeling Some Biological Phenomena}, journal = {Journal of Partial Differential Equations}, year = {2011}, volume = {24}, number = {1}, pages = {1--14}, abstract = {

In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N=1, the global existence of the weak solution will be established by the bootstrap argument.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v24.n1.1}, url = {http://global-sci.org/intro/article_detail/jpde/5194.html} }
TY - JOUR T1 - Nonlinear Hyperbolic-parabolic System Modeling Some Biological Phenomena AU - Shaohua Wu & Hua Chen JO - Journal of Partial Differential Equations VL - 1 SP - 1 EP - 14 PY - 2011 DA - 2011/02 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n1.1 UR - https://global-sci.org/intro/article_detail/jpde/5194.html KW - Hyperbolic-parabolic system KW - chemosensitive movement KW - external signal KW - global existence AB -

In this paper, we study a nonlinear hyperbolic-parabolic system modeling some biological phenomena. By semigroup theory and Leray-Schauder fixed point argument, the local existence and uniqueness of the weak solutions for this system are proved. For the spatial dimension N=1, the global existence of the weak solution will be established by the bootstrap argument.

Shaohua Wu and Hua Chen. (2011). Nonlinear Hyperbolic-parabolic System Modeling Some Biological Phenomena. Journal of Partial Differential Equations. 24 (1). 1-14. doi:10.4208/jpde.v24.n1.1
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