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Displaying 21 – 27 of 27

Blow-up results for some reaction-diffusion equations with time delay

Hongliang Wang, Yujuan Chen, Haihua Lu (2012)

Annales Polonici Mathematici

We discuss the effect of time delay on blow-up of solutions to initial-boundary value problems for nonlinear reaction-diffusion equations. Firstly, two examples are given, which indicate that the delay can both induce and prevent the blow-up of solutions. Then we show that adding a new term with delay may not change the blow-up character of solutions.

Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

S. Ibrahim, A. Lyaghfouri (2012)

Mathematical Modelling of Natural Phenomena

In this paper, we show finite time blow-up of solutions of the p−wave equation in ℝN, with critical Sobolev exponent. Our work extends a result by Galaktionov and Pohozaev [4]

Blow-up versus global existence of solutions to aggregation equations

Grzegorz Karch, Kanako Suzuki (2011)

Applicationes Mathematicae

A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.

Boundary blow-up solutions for a cooperative system involving the p-Laplacian

Li Chen, Yujuan Chen, Dang Luo (2013)

Annales Polonici Mathematici

We study necessary and sufficient conditions for the existence of nonnegative boundary blow-up solutions to the cooperative system $Δ_{p} u = g (u - α v), Δ_{p} v = f (v - β u)$ in a smooth bounded domain of $ℝ^{N}$ , where $Δ_{p}$ is the p-Laplacian operator defined by $Δ_{p} u = {d i v (| \nabla u |}^{p - 2} \nabla u)$ with p > 1, f and g are nondecreasing, nonnegative C¹ functions, and α and β are two positive parameters. The asymptotic behavior of solutions near the boundary is obtained and we get a uniqueness result for p = 2.

Boundary blow-up solutions of cooperative systems

Juan Dávila, Louis Dupaigne, Olivier Goubet, Salomé Martínez (2009)

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

Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case.

Weiss, Georg S. (2004)

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

Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents

Manuel del Pino, Fethi Mahmudi, Monica Musso (2014)

Journal of the European Mathematical Society

Let $Ω$ be a bounded domain in $ℝ^{n}$ with smooth boundary $\partial Ω$ . We consider the equation $d^{2} Δ u - u + u^{\frac{n - k + 2}{n - k - 2}} = 0 in Ω$ , under zero Neumann boundary conditions, where $Ω$ is open, smooth and bounded and $d$ is a small positive parameter. We assume that there is a $k$ -dimensional closed, embedded minimal submanifold $K$ of $\partial Ω$ , which is non-degenerate, and certain weighted average of sectional curvatures of $\partial Ω$ is positive along $K$ . Then we prove the existence of a sequence $d = d_{j} \to 0$ and a positive solution $u_{d}$ such that $d^{2} {| \nabla u_{d} |}^{2} ⇀ S δ_{K} as d \to 0$ in the sense of measures, where $δ_{K}$ ...

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