Abstract.
We consider the general nonlinear heat equation \(\partial_t u = \Delta u +a|u|^{p_1-1}u+g(u), u(0)=\varphi,\) on \((0,\infty)\times I\!\!R^n ,\) where \(a\in I\!\!R, p_1>1+(2/n)\) and g satisfies certain growth conditions. We prove the existence of global solutions for small initial data with respect to a norm which is related to the structure of the equation. We also prove that some of those global solutions are asymptotic for large time to self-similar solutions of the single power nonlinear heat equation, i.e. with \(g\equiv 0.\)
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Received: 23 July 1999 / Accepted: 14 December 2000 / Published online: 23 July 2001
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Snoussi, S., Tayachi, S. & Weissler, F. Asymptotically self-similar global solutions of a general semilinear heat equation. Math Ann 321, 131–155 (2001). https://doi.org/10.1007/PL00004498
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DOI: https://doi.org/10.1007/PL00004498