Instability of a Parabolic Equation with a Quadratic Nonlinearity
نویسنده
چکیده
A nonlinear parabolic differential equation with a quadratic nonlinearity is presented which has at least one equilibrium. The linearization about this equilibrium is asymptotically stable, but by using a technique inspired by H. Fujita, we show that the equilibrium is unstable in the nonlinear setting. The perturbations used have the property that they are small in every L p norm, yet they result in solutions which fail to be global.
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تاریخ انتشار 2008