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Blow-up phenomena for nonlinear pseudo-parabolic equations with gradient term
Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity
Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan |
$\left\{ {\begin{array}{*{20}{l}}{{u_t} = {d_1}\Delta u - \nabla \cdot (u{\chi _1}(w)\nabla w) + {\mu _1}u(1 - u - {a_1}v)}&{;{\rm{in}}\;\Omega \times (0,\infty ),}\\{{v_t} = {d_2}\Delta v - \nabla \cdot (v{\chi _2}(w)\nabla w) + {\mu _2}v(1 - {a_2}u - v)}&{;{\rm{in}}\;\Omega \times (0,\infty ),}\\{{w_t} = {d_3}\Delta w + h(u,v,w)}&{;{\rm{in}}\;\Omega \times (0,\infty ),}\end{array}} \right.$ |
$\Omega$ |
$\mathbb{R}^n$ |
$\partial \Omega$ |
$n\in \mathbb{N}$ |
$h$ |
$\chi_i$ |
$\chi_i(w)=\chi_i$ |
$\mu_1, \mu_2$ |
$\mu_1, \mu_2$ |
References:
show all references
References:
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