Results 31 to 40 of about 760 (78)

Blow-up of Solutions to the Generalized Inviscid Proudman-Johnson Equation [PDF]

J. Math Fluid Mech, 15, 3 (2013), 493-523, 2013
For arbitrary values of a parameter $\lambda\in R$, finite-time blow-up of solutions to the generalized, inviscid Proudman-Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem.
arxiv   +1 more source

Extremals for Fractional Moser–Trudinger Inequalities in Dimension 1 via Harmonic Extensions and Commutator Estimates

Advanced Nonlinear Studies, 2020
We prove the existence of extremals for fractional Moser–Trudinger inequalities in an interval and on the whole real line. In both cases we use blow-up analysis for the corresponding Euler–Lagrange equation, which requires new sharp estimates obtained ...
Mancini Gabriele, Martinazzi Luca
doaj   +1 more source

Blow-up for the two-component Camassa-Holm system [PDF]

Discrete Contin. Dyn. Syst. 35, 2041-2051 (2015), 2014
Following conservative solutions of the two-component Camassa-Holm system $u_t-u_{txx}+3uu_x-2u_xu_{xx}-uu_{xxx}+\rho\rho_x=0$, $\rho_t+(u\rho)_x=0$ along characteristics, we determine if wave breaking occurs in the nearby future or not, for initial data $u_0\in H^1(\mathbb R)$ and $\rho_0\in L^2(\mathbb R)$.
arxiv   +1 more source

Blow-up of solutions to cubic nonlinear Schrödinger equations with defect: The radial case

Advances in Nonlinear Analysis, 2017
In this article we investigate both numerically and theoretically the influence of a defect on the blow-up of radial solutions to a cubic NLS equation in dimension 2.
Goubet Olivier, Hamraoui Emna
doaj   +1 more source

Positive Solutions for Systems of Quasilinear Equations with Non-homogeneous Operators and Weights

Advanced Nonlinear Studies, 2020
In this paper we deal with positive radially symmetric solutions for a boundary value problem containing a strongly nonlinear operator. The proof of existence of positive solutions that we give uses the blow-up method as a main ingredient for the search ...
García-Huidobro Marta, Manasevich Raúl, Tanaka Satoshi   +2 more
doaj   +1 more source

Blow-up of solutions for Euler-Bernoulli equation with nonlinear time delay

Open Mathematics
We study the Euler-Bernoulli equations with time delay: utt+Δ2u−g1∗Δ2u+g2∗Δu+μ1ut(x,t)∣ut(x,t)∣m−2+μ2ut(x,t−τ)∣ut(x,t−τ)∣m−2=f(u),{u}_{tt}+{\Delta }^{2}u-{g}_{1}\ast {\Delta }^{2}u+{g}_{2}\ast \Delta u+{\mu }_{1}{u}_{t}\left(x,t){| {u}_{t}\left(x,t ...
Lin Rongrui, Gao Yunlong, She Lianbing
doaj   +1 more source

Coercive elliptic systems with gradient terms

Advances in Nonlinear Analysis, 2017
In this paper we give a classification of positive radial solutions of the following system:
Filippucci Roberta, Vinti Federico
doaj   +1 more source

Sign-Changing Solutions for the One-Dimensional Non-Local sinh-Poisson Equation

Advanced Nonlinear Studies, 2020
We study the existence of sign-changing solutions for a non-local version of the sinh-Poisson equation on a bounded one-dimensional interval I, under Dirichlet conditions in the exterior of I.
DelaTorre Azahara, Mancini Gabriele, Pistoia Angela   +2 more
doaj   +1 more source

Errata: Scattering threshold for the focusing nonlinear Klein-Gordon equation [PDF]

Anal. PDE 9 (2016) 503-514, 2015
This article resolves some errors in the paper "Scattering threshold for the focusing nonlinear Klein-Gordon equation", Analysis & PDE 4 (2011) no. 3, 405-460. The errors are in the energy-critical cases in two and higher dimensions.
arxiv   +1 more source

Initial Blow-up of Solutions of Semilinear Parabolic Inequalities [PDF]

arXiv, 2009
We obtain an upper bound on the initial blow-up of nonnegative solutions of second order semilinear parabolic inequalities when a superlinear exponent in the inequalities is not too large.
arxiv