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Displaying 21 – 40 of 120

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]

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 $δ_{K}$ ...

Changing blow-up time in nonlinear Schrödinger equations

Rémi Carles (2003)

Journées équations aux dérivées partielles

Solutions to nonlinear Schrödinger equations may blow up in finite time. We study the influence of the introduction of a potential on this phenomenon. For a linear potential (Stark effect), the blow-up time remains unchanged, but the location of the collapse is altered. The main part of our study concerns isotropic quadratic potentials. We show that the usual (confining) harmonic potential may anticipate the blow-up time, and always does when the power of the nonlinearity is $L^{2}$ -critical. On the other...

Conformal metrics with constant $Q$ -curvature.

Malchiodi, Andrea (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Critical boundary constants and Pohozaev identity

Ould Ahmed-Izid-Bih Isselkou (2001)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Critical exponent and minimization problem in $ℝ^{N}$

Samira Benmouloud-Sbai, Mohamed Guedda (2003)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Critical global asymptotics in higher-order semilinear parabolic equations.

Galaktionov, Victor A. (2003)

International Journal of Mathematics and Mathematical Sciences

Critical Neumann problem with competing Hardy potentials.

Daomin Cao, Jan Chabrowski (2007)

Revista Matemática Complutense

Critical nonlinear elliptic equations with singularities and cylindrical symmetry

Marino Badiale, Enrico Serra (2004)

Revista Matemática Iberoamericana

Motivated by a problem arising in astrophysics we study a nonlinear elliptic equation in RN with cylindrical symmetry and with singularities on a whole subspace of RN. We study the problem in a variational framework and, as the nonlinearity also displays a critical behavior, we use some suitable version of the Concentration-Compactness Principle. We obtain several results on existence and nonexistence of solutions.

Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws

Piotr Biler, Grzegorz Karch, Wojbor A Woyczyński (2001)

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

Critical singular problems on unbounded domains.

de Morais Filho, D.C., Miyagaki, O.H. (2005)

Abstract and Applied Analysis

Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type

Takayoshi Ogawa (2006)

Banach Center Publications

We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.

Elliptic equations with critical Sobolev exponents in dimension 3

Olivier Druet (2002)

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

Energy and Morse index of solutions of Yamabe type problems on thin annuli

Mohammed Ben Ayed, Khalil El Mehdi, Mohameden Ould Ahmedou, Filomena Pacella (2005)

Journal of the European Mathematical Society

We consider the Yamabe type family of problems $(P_{ε}) : - Δ u_{ε} = u_{ε}^{(n + 2) / (n - 2)}$ , $u_{ε} > 0$ in $A_{ε}$ , $u_{ε} = 0$ on $\partial A_{ε}$ , where $A_{ε}$ is an annulus-shaped domain of $ℝ^{n}$ , $n \geq 3$ , which becomes thinner as $ε \to 0$ . We show that for every solution $u_{ε}$ , the energy $\int_{A_{ε}} | \nabla u_{|}^{2}$ as well as the Morse index tend to infinity as $ε \to 0$ . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on $ℝ^{n}$ , a half-space or an infinite strip. Our argument also involves a Liouville type theorem...

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