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math.AP2014★ 5 cited
Linear profile decompositions for a family of fourth order Schrödinger equations
Jincheng Jiang, Shuanglin Shao, Betsy Stovall
We establish linear profile decompositions for the fourth order Schrödinger equation and for certain fourth order perturbations of the Schrödinger equation, in dimensions greater t…
math.AP2012★ 4 cited
Blowup behaviour for the nonlinear Klein--Gordon equation
Rowan Killip, Betsy Stovall, Monica Visan
We analyze the blowup behaviour of solutions to the focusing nonlinear Klein--Gordon equation in spatial dimensions . We obtain upper bounds on the blowup rate, both globa…
math.AP2010★ 2 cited
Scattering for the cubic Klein--Gordon equation in two space dimensions
Rowan Killip, Betsy Stovall, Monica Visan
We consider both the defocusing and focusing cubic nonlinear Klein--Gordon equations in two space dimensions for real-valued initial data $u(0)\in…