Study of global solutions of parabolic equations via a priori estimates. Part I: Equations with principal elliptic part equal to the laplacian |
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Authors: | Gary M. Lieberman |
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Abstract: | We study global solutions of ut=Δu + f(u, Du) with zero boundary data. Under suitable hypotheses on f, we show that an energy, which is roughly the H1 norm of u, cannot change too rapidly. When f depends only on u, this estimate implies that all global solutions are bounded. |
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