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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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References:
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