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Asymptotic Behavior of a 3D Chemotaxis-Stokes Predator-Prey System Incorporating Logistic Growth
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DOI：10.1007/s00245-026-10404-4.png)
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Abstract
En 中文
-> This article primarily investigates the convergence rates of solutions to the chemotaxis-Stokes system, which consists of two distinct species represented by the following system { u1(t) + w & centerdot; del u(1) = del u(1)-chi del & centerdot; (u(1 )del v(1))+u(1)(lambda(1)-mu(1)u(1) +au(2)), x is an element of Omega, t >0, u2(t) + w & centerdot; del u(2) = del u(2) + xi del & centerdot; (u(2)del v(2))+u(2)(lambda(2)-mu(2)u(2)-bu(1)), x is an element of Omega, t > 0, v1(t )+ w & centerdot; del v(1) = del v(1)-v(1) + u(2), x is an element of Omega , t > 0, w & centerdot; del v(2)= del v(2)-v(2) + u(1), x is an element of Omega,t > 0, w(t) +del P= del w + (u(1) +u(2))del phi, x is an element of Omega,t > 0, del & centerdot;w= 0, x is an element of Omega,t > 0, subject to homogeneous Neumann boundary conditions within a smooth bounded domain Omega subset of R-3. By formulating a suitable energy functional, the following results are established: center dot If lambda(2)mu(1) > b lambda(1) and both mu(1) and mu(2) are sufficiently large, it is demonstrated that for any global bounded solution originating from adequately regular initial data with u(10), u(20) equivalent to/ 0, (u(1), u(2), v(1), v(2), w)(& centerdot;, t)->(u(1*), u(2*), u(2*), u(1*), 0) uniformly in Omega as t -infinity, where (u(1*), u(2*), u(2*), u(1*), 0) denotes the unique positive spatially homogeneous equilibrium of this system. center dot If lambda(2)mu(1) <= b lambda(1) and mu(1) is sufficiently large, then all global bounded solutions with reasonably smooth initial data satisfying u(10) equivalent to/ 0 exhibit the following behavior: (u(1), u(2), v(1), v(2), w)(& centerdot;, t) -> (lambda(1)/mu(1),0, 0, lambda(1)/mu(1),0) uniformly on Omega as t -> infinity.
Keywords:
Chemotaxis-Stokes
Predator-prey
Logistic source
Convergence rates
Large time behavior
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1.7
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106
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