Existence of L
1-Connections Between Equilibria of a Semilinear Parabolic Equation |
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| Authors: | Marek Fila Hiroshi Matano Peter Poláčik |
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| Institution: | (1) Institute of Applied Mathematics, Comenius University, 842 48 Bratislava, Slovakia;(2) Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo, 153-8914, Japan;(3) School of Mathematics, University of Minnesota, Minneapolis, Minneapolis, 55455 |
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| Abstract: | We give a necessary and sufficient condition for the existence of L
1-connections between equilibria of a semilinear parabolic equation. By an L
1-connection from an equilibrium 
– to an equilibrium
+ we mean a function u( , t) which is a classical solution on the interval (– , T) for some T   and blows up at t = T but continues to exist in the space L
1 for t T, ) and satisfies u(, t) 
± (in a suitable sense) as t ±. The main tool in our analysis is the zero number. |
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| Keywords: | Semilinear parabolic equation L
1-connections nonlinear heat equation blow-up connecting orbits zero number |
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