## Non-unicité des solutions d’une équation d’évolution non- linéaire.(French)Zbl 0553.35046

Author’s summary: We prove a non-uniqueness result for a semi-linear parabolic equation. If $$\gamma >1$$ and N an integer such that $$1<N(\gamma -1)/2<\inf (\gamma,(\gamma +3)/2))$$ and $$\Omega$$ is a ball of $${\mathbb{R}}^ N$$, then the equation $$\partial u/\partial t-\Delta u=u| u|^{\gamma -1},\quad u(0)=u_ 0,\quad u|_{\partial \Omega}=0$$ possesses an infinite number of solutions such that $$\lim_{t\to 0}\| u(t)-u_ 0\|_ q=0$$ where $$1\leq q<N(\gamma - 1)/2$$.