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11 papers · 2 filters
Universality of blow up profile for small blow up solutions to the energy critical wave map equation
Thomas Duyckaerts, Hao Jia, Carlos Kenig +1
In this paper we introduce the channel of energy argument to the study of energy critical wave maps into the sphere. More precisely, we prove a channel of energy type inequality fo…
A modulation technique for the blow-up profile of the vector-valued semilinear wave equation
Asma Azaiez, Hatem Zaag
We consider a vector-valued blow-up solution with values in for the semilinear wave equation with power nonlinearity in one space dimension (this is a system of PDEs…
Isotropy prohibits the loss of strong ellipticity through homogenization in linear elasticity
Gilles Francfort, Antoine Gloria
Since the seminal contribution of Geymonat, M{ü}ller, and Triantafyllidis, it is known that strong ellipticity is not necessarily conserved by homogenization in linear elasticity.…
Analysis of the loss of boundary conditions for the diffusive Hamilton-Jacobi equation
Alessio Porretta, Philippe Souplet
We consider the diffusive Hamilton-Jacobi equation, with homogeneous Dirichlet conditions and regular initial data. It is known from [Barles-DaLio, 2004] that the problem admits a…
On local smoothing problems and Stein's maximal spherical means
Changxing Miao, Jianwei Yang, Jiqiang Zheng
It is proved that the local smoothing conjecture for wave equations implies certain improvements on Stein's analytic family of maximal spherical means. Some related problems are al…
Excluding blowup at zero points of the potential by means of Liouville-type theorems
Jong-Shenq Guo, Philippe Souplet
We prove a local version of a (global) result of Merle and Zaag about ODE behavior of solutions near blowup points for subcritical nonlinear heat equations. As an application, for…