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The Glassey conjecture with radially symmetric data
Glassey conjecture semilinear wave equations Morawetz estimates KSS estimates
2011/8/25
Abstract: In this paper, we verify the Glassey conjecture in the radial case for all spatial dimensions, which states that, for the nonlinear wave equations of the form $\Box u=|\nabla u|^p$, the crit...
Radially symmetric and azimuthally modulated vortex solitons supported by localized gain
Radially symmetric azimuthally modulated vortex solitons localized gain
2010/12/28
We discover that a spatially localized gain supports stable vortex solitons in media with cu-bic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying r...
Radially symmetric minimizers for a $p$-Ginzburg Landau type energy in $\R^2$
Radially symmetric minimizers math
2010/11/17
We consider the minimization of a p-Ginzburg-Landau energy functional over the class of radially symmetric functions of degree one. We prove the existence of a unique minimizer in this class, and sho...
