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We consider the semilinear Lane–Emden problem where $p > 1$ and $Ω$ is a smooth bounded domain of $ℝ^{2}$ . The aim of the paper is to analyze the asymptotic behavior of sign changing solutions of $(_{p})$ , as $p \to + \infty$ . Among other results we show, under some symmetry assumptions on $Ω$ , that the positive and negative parts of a family of symmetric solutions concentrate at the same point, as $p \to + \infty$ , and the limit profile looks like a tower of two bubbles given by a superposition of a regular and a singular solution of the Liouville...

Asymptotic behavior of a predator-prey diffusion system with time delays.

Meng, Yijie, Wang, Yifu (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Asymptotic behaviour for the solution of the compressible Navier-Stokes equation, when the compressibility goes to zero

Stéphane Added, Hélène Added (1987)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Asymptotic behaviour of solutions of some semilinear parabolic problems

Luis Herraiz (1999)

Annales de l'I.H.P. Analyse non linéaire

Asymptotic behaviour of the solutions of a strongly nonlinear parabolic problem

M. A. Herrero, J. L. Vazquez (1981)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Asymptotic estimates for PDE with $p$ -Laplacian and damping.

Mařík, Robert (2005)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Asymptotic periodicity of positive solutions of reaction diffusion equations on a ball.

Peter Polácik, Xu-Yan Chen (1996)

Journal für die reine und angewandte Mathematik

Asymptotics for quasilinear equations with nearly critical growth.

Marhrani El-Miloudi, Alain Brillard (1997)

Extracta Mathematicae

Asymptotics of parabolic equations with possible blow-up

Radosław Czaja (2004)

Colloquium Mathematicae

We describe the long-time behaviour of solutions of parabolic equations in the case when some solutions may blow up in a finite or infinite time. This is done by providing a maximal compact invariant set attracting any initial data for which the corresponding solution does not blow up. The abstract result is applied to the Frank-Kamenetskii equation and the N-dimensional Navier-Stokes system with small external force.

Asymptotics of the first nodal line

Daniel Grieser, David Jerison (1995)

Journées équations aux dérivées partielles

Asymptotics of the Nodal Lines of Solutions of 2-Dimensional Schrödinger Equations.

M. Hoffmann-Ostenhof (1988)

Mathematische Zeitschrift

Averaging techniques and oscillation of quasilinear elliptic equations

Zhi-Ting Xu, Bao-Guo Jia, Shao-Yuan Xu (2004)

Annales Polonici Mathematici

By using averaging techniques, some oscillation criteria for quasilinear elliptic differential equations of second order $\sum_{i, j = 1}^{N} D_{i} [A_{i j} {(x) | D y |}^{p - 2} D_{j} y] + p (x) f (y) = 0$ are obtained. These results extend and generalize the criteria for linear differential equations due to Kamenev, Philos and Wong.

Behaviour of symmetric solutions of a nonlinear elliptic field equation in the semi-classical limit: Concentration around a circle.

D'Aprile, Teresa (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

"Best possible'' maximum principles

L. E. Payne (1985)

Banach Center Publications

Blow-up behavior in nonlocal vs local heat equations

Philippe Souplet (2000)

Banach Center Publications

We present some recent results on the blow-up behavior of solutions of heat equations with nonlocal nonlinearities. These results concern blow-up sets, rates and profiles. We then compare them with the corresponding results in the local case, and we show that the two types of problems exhibit "dual" blow-up behaviors.

Blowup estimates for a mutualistic model in ecology.

Lin, Zhigui (2002)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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