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The journal Asymptotic Analysis fulfills a twofold function. It aims at publishing original mathematical results in the asymptotic theory of problems affected by the presence of small or large parameters on the one hand, and at giving specific indications of their possible applications to different fields of natural sciences on the other hand.
Asymptotic Analysis thus provides mathematicians with a concentrated source of newly acquired information which they may need in the analysis of asymptotic problems.
Authors: Nimi, Aymard Christbert | Langa, Franck Davhys Reval
Article Type: Research Article
Abstract: In this article, our objective is to explore a Cahn–Hilliard system with a proliferation term, particularly relevant in biological contexts, with Neumann boundary conditions. We commence our investigation by establishing the boundedness of the average values of the local cell density u and the temperature H . This observation suggests that the solution ( u , H ) either persists globally in time or experiences finite-time blow-up. Subsequently, we prove the convergence of u to 1 and H to 0 as time approaches infinity. Finally, we bolster our theoretical findings with numerical simulations.
Keywords: Cahn–Hilliard system, proliferation term, dissipativity, blow up, simulations
DOI: 10.3233/ASY-241915
Citation: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-23, 2024
Authors: Moutinho, Abdon
Article Type: Research Article
Abstract: In this paper, we consider the problem of elasticity and stability of the collision of two kinks with low speed v for the nonlinear wave equation known as the ϕ 6 model in dimension 1 + 1 . We construct a sequence of approximate solutions ( ϕ k ( v , t , x ) ) k ∈ N ⩾ 2 for this model to understand the effects of the collision in the movement of each soliton during a …large time interval. The construction uses a new asymptotic method which is not only restricted to the ϕ 6 model. Show more
Keywords: Kink, soliton, ϕ6 model, non-integrable model, scalar field, partial differential equation, ordinary differential equation, collision
DOI: 10.3233/ASY-241917
Citation: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-90, 2024
Authors: Coclite, Giuseppe Maria | di Ruvo, Lorenzo
Article Type: Research Article
Abstract: The wave propagation in dilatant granular materials is described by a nonlinear evolution equation of the fifth order deduced by Giovine–Oliveri in (Meccanica 30 (4) (1995 ) 341–357). In this paper, we study the well-posedness of the classical solutions for the Cauchy problem, associated with this equation.
Keywords: Existence, Uniqueness, Stability, Wave propagation, Dilatant granular materials, Cauchy problem
DOI: 10.3233/ASY-241920
Citation: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-28, 2024
Authors: Shen, Liejun | Squassina, Marco
Article Type: Research Article
Abstract: We consider the existence of ground state solutions for a class of zero-mass Chern–Simons–Schrödinger systems − Δ u + A 0 u + ∑ j = 1 2 A j 2 u = f ( u ) − a ( x ) | u | p − 2 u , ∂ 1 A 2 − ∂ 2 A 1 = − 1 2 | u …| 2 , ∂ 1 A 1 + ∂ 2 A 2 = 0 , ∂ 1 A 0 = A 2 | u | 2 , ∂ 2 A 0 = − A 1 | u | 2 , where a : R 2 → R + is an external potential, p ∈ ( 1 , 2 ) and f ∈ C ( R ) denotes the nonlinearity that fulfills the critical exponential growth in the Trudinger–Moser sense at infinity. By introducing an improvement of the version of Trudinger–Moser inequality approached in (J. Differential Equations 393 (2024 ) 204–237), we are able to investigate the existence of positive ground state solutions for the given system using variational method. Show more
Keywords: Zero-mass, Chern–Simons–Schrödinger system, Trudinger–Moser inequality, Critical exponential growth, Ground state solution, Variational method
DOI: 10.3233/ASY-241921
Citation: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-25, 2024
Authors: Ramos, A.J.A. | Rosário, L.G.M. | Campelo, A.D.S. | Freitas, M.M. | Martins, J.D.
Article Type: Research Article
Abstract: In the literature, we can find many studies that investigate the so-called truncated version of the Timoshenko beam system. In general, the truncated version eliminates the second spectrum of velocity and therefore does not require equal wave velocities to achieve exponential decay. However, the truncated system does not satisfy a Cauchy problem, which makes studying its qualitative properties more challenging. In this article, we present the truncated version of the laminated beam system. Our main results are the well-posedness of the problem using the classical Faedo-Galerkin method combined with a priori estimates and the exponential …decay of the energy functional without requiring equal wave velocities. Show more
Keywords: Laminated beams, truncated system, well-posedness, exponential decay
DOI: 10.3233/ASY-241918
Citation: Asymptotic Analysis, vol. Pre-press, no. Pre-press, pp. 1-23, 2024
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