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- W2013117525 abstract "In this paper we study the existence and the stability of bounded solutions of the following non-linear system of parabolic equations with homogeneous Dirichlet boundary conditions: ut=DΔu+f(t,u),t⩾0,u∈Rn,u=0on∂Ω, where f∈C1(R×Rn), D=diag(d1,d2,…,dn) is a diagonal matrix with di>0, i=1,2,…,n, and Ω is a sufficiently regular bounded domain in RN(N=1,2,3). Roughly speaking we shall prove the following result: if f is globally Lipschitz with constant L, 34<α<1and(λ1d)1−αΓ(1−α)>6ML, then the system has a bounded solution on Rn which is stable, where 2d=min{di:i=1,2,…,n}, (λjdit)αe−λj(di/2)t<M, λi are the eigenvalues of −Δ, and Γ(·) is the well-known gamma function. Also, we prove that for a large class of functions f this bounded solution is almost periodic." @default.
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- W2013117525 date "2003-03-01" @default.
- W2013117525 modified "2023-10-03" @default.
- W2013117525 title "Existence and stability of bounded solutions for a system of parabolic equations" @default.
- W2013117525 cites W1989501012 @default.
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- W2013117525 doi "https://doi.org/10.1016/s0022-247x(03)00025-8" @default.
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