Asymptotically periodic solutions for a class of nonlinear coupled oscillators.
The Cauchy problem for the nonlinear Schrödinger Equation in H1.
Regular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state
Poincaré's inequality and global solutions of a nonlinear parabolic equation
Universal solutions of a nonlinear heat equation on
In this paper, we study the relationship between the long time behavior of a solution of the nonlinear heat equation on (where ) and the asymptotic behavior as of its initial value . In particular, we show that if the sequence of dilations converges weakly to as , then the rescaled solution converges uniformly on to along the subsequence , where is an appropriate flow. Moreover, we show there exists an initial value such that the set of all possible attainable in this...
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