Boundedness in a quasilinear chemotaxis–haptotaxis system with logistic source

Ji Liu; Jiashan Zheng; Yifu Wang

doi:10.1007/s00033-016-0620-8

Boundedness in a quasilinear chemotaxis–haptotaxis system with logistic source

Ji Liu, Jiashan Zheng, Yifu Wang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

In this paper, we consider the quasilinear chemotaxis–haptotaxis system (Formula presented.) in a bounded smooth domain (Formula presented.) under zero-flux boundary conditions, where the nonlinearities (Formula presented.) and (Formula presented.) are assumed to generalize the prototypes(Formula presented.)with (Formula presented.) and (Formula presented.) fulfills(Formula presented.),where (Formula presented.) Assuming nonnegative initial data (Formula presented.) and (Formula presented.) for some (Formula presented.) we prove that (i) for (Formula presented.) if (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded, (ii) for (Formula presented.) if (Formula presented.) and (Formula presented.) or (Formula presented.) and (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded.

Original language	English
Article number	21
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	67
Issue number	2
DOIs	https://doi.org/10.1007/s00033-016-0620-8
Publication status	Published - 1 Apr 2016

Keywords

Boundedness
Chemotaxis
Haptotaxis
Logistic source
Quasilinear

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10.1007/s00033-016-0620-8

Cite this

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abstract = "In this paper, we consider the quasilinear chemotaxis–haptotaxis system (Formula presented.) in a bounded smooth domain (Formula presented.) under zero-flux boundary conditions, where the nonlinearities (Formula presented.) and (Formula presented.) are assumed to generalize the prototypes(Formula presented.)with (Formula presented.) and (Formula presented.) fulfills(Formula presented.),where (Formula presented.) Assuming nonnegative initial data (Formula presented.) and (Formula presented.) for some (Formula presented.) we prove that (i) for (Formula presented.) if (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded, (ii) for (Formula presented.) if (Formula presented.) and (Formula presented.) or (Formula presented.) and (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded.",

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AU - Zheng, Jiashan

AU - Wang, Yifu

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N2 - In this paper, we consider the quasilinear chemotaxis–haptotaxis system (Formula presented.) in a bounded smooth domain (Formula presented.) under zero-flux boundary conditions, where the nonlinearities (Formula presented.) and (Formula presented.) are assumed to generalize the prototypes(Formula presented.)with (Formula presented.) and (Formula presented.) fulfills(Formula presented.),where (Formula presented.) Assuming nonnegative initial data (Formula presented.) and (Formula presented.) for some (Formula presented.) we prove that (i) for (Formula presented.) if (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded, (ii) for (Formula presented.) if (Formula presented.) and (Formula presented.) or (Formula presented.) and (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded.

AB - In this paper, we consider the quasilinear chemotaxis–haptotaxis system (Formula presented.) in a bounded smooth domain (Formula presented.) under zero-flux boundary conditions, where the nonlinearities (Formula presented.) and (Formula presented.) are assumed to generalize the prototypes(Formula presented.)with (Formula presented.) and (Formula presented.) fulfills(Formula presented.),where (Formula presented.) Assuming nonnegative initial data (Formula presented.) and (Formula presented.) for some (Formula presented.) we prove that (i) for (Formula presented.) if (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded, (ii) for (Formula presented.) if (Formula presented.) and (Formula presented.) or (Formula presented.) and (Formula presented.) then (Formula presented.) has a unique nonnegative classical solution which is globally bounded.

KW - Boundedness

KW - Chemotaxis

KW - Haptotaxis

KW - Logistic source

KW - Quasilinear

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Boundedness in a quasilinear chemotaxis–haptotaxis system with logistic source

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