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Time asymptotic description of an abstract Cauchy problem solution and application to transport equation

Boulbeba Abdelmoumen, Omar Jedidi, Aref Jeribi (2014)

Applications of Mathematics

In this paper, we study the time asymptotic behavior of the solution to an abstract Cauchy problem on Banach spaces without restriction on the initial data. The abstract results are then applied to the study of the time asymptotic behavior of solutions of an one-dimensional transport equation with boundary conditions in L 1 -space arising in growing cell populations and originally introduced by M. Rotenberg, J. Theoret. Biol. 103 (1983), 181–199.

Topological tools for the prescribed scalar curvature problem on S n

Dina Abuzaid, Randa Ben Mahmoud, Hichem Chtioui, Afef Rigane (2014)

Open Mathematics

In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

Transition from decay to blow-up in a parabolic system

Pavol Quittner (1998)

Archivum Mathematicum

We show a locally uniform bound for global nonnegative solutions of the system u t = Δ u + u v - b u , v t = Δ v + a u in ( 0 , + ∞ ) × Ω , u = v = 0 on ( 0 , + ∞ ) × ∂ Ω , where a > 0 , b ≥ 0 and Ω is a bounded domain in ℝ n , n ≤ 2 . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

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