A quasilinear chemotaxis-haptotaxis model: The roles of nonlinear diffusion and logistic source

作者：Liu, Ji^*; Wang, Yifu

来源：Mathematical Methods in the Applied Sciences, 2017, 40(6): 2107-2121.

DOI：10.1002/mma.4126

• chemotaxis
• haptotaxis
• quasilinear
• boundedness
• logistic source

In this paper, we study the following quasilinear chemotaxis- haptotaxis system
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in a bounded smooth domain Omega subset of R-n (n >= 1) under zero-flux boundary conditions, where the nonlinearities D, S-1, and S-2 are supposed to generalize the prototypes
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with C-D, C-S1, C-S2 > 0, m, q(1), q(2) is an element of R, and f is an element of C-1 ([0, +infinity) x [0, +infinity)) satisfies
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(i) For n = 1, if q(1) < m/2 + 1 and q(2) < min {m/2 + 1, 2}, then (star) has a unique nonnegative classical solution, which is globally bounded.
(ii) For n = 2, if q(1) < m+1/2 and q(2) < min {m/2 + 1, 3/2}, then (star) has a unique nonnegative classical solution, which is globally bounded.
(iii) For n >= 3, if q(1) < m/2 + 2/n+2 and q(2) < min {m/2 + 1, 2 - n-2/n+2}, then (star) has a unique nonnegative classical solution, which is globally bounded.

• 出版日期2017-4
• 单位北京理工大学