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Formal solutions of semilinear heat equations |
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| Authors: | Grzegorz ?ysik S?awomir Michalik |
| Institution: | a Institute of Mathematics, Polish Academy of Sciences, ?niadeckich 8, 00-956 Warsaw 10, Poland b ?wi?tokrzyska Academy, Kielce, Poland c Faculty of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszyński University, Dewajtis 5, 01-815 Warsaw, Poland |
| Abstract: | We study formal power series solutions to the initial value problem for semilinear heat equation t∂u−Δu=f(u) with polynomial nonlinearity f and prove that they belong to the formal Gevrey class G2. Next we give counterexamples showing that the solution, in general, is not analytic in time at t=0. |
| Keywords: | Semilinear heat equation Formal solutions Gevrey estimates Nonanalyticity |
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