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Metastable patterns in solutions of \(u_ t=\epsilon ^ 2u_{xx}-f(u)\). (English) Zbl 0685.35054
On étudie solutions de l’équation \(u_ t=\epsilon^ 2u_{xx}- f(u),\) pour \(0\leq x\leq 1\), \(t>0\), satisfaisantes les conditions aux limites de Neumann \(u_ x(0,t)=0\), \(u_ x(1,t)=0.\)
La fonction f est régulière et satisfait les conditions \(f(\pm 1)=0\), \(f'(\pm 1)>0\), \(\int^{1}_{-1}f(u)du=0.\)
On donne la définition d’états métastables (cfr. le mémoire); on étudie en détail l’existence et la persistance de telles états; on étudie aussi le temps de vie de ces solutions.

MSC:
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
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