Baras, Pierre Non-unicité des solutions d’une équation d’évolution non- linéaire. (French) Zbl 0553.35046 Ann. Fac. Sci. Toulouse, V. Sér., Math. 5, 287-302 (1983). 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 \(1\leq q<N(\gamma - 1)/2\). Reviewer: R.Badescu Cited in 20 Documents MSC: 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:non-uniqueness; semi-linear parabolic equation; infinite number of solutions PDF BibTeX XML Cite \textit{P. Baras}, Ann. Fac. Sci. Toulouse, Math. (5) 5, 287--302 (1983; Zbl 0553.35046) Full Text: DOI Numdam EuDML OpenURL References: [1] Baras, P.. «Compacité de l’opérateur f → u solution d’une équation non linéaire (du/dt) + Au ∋ f». Note au C.R.A.S., t. 286, série A, (1978), p. 1113-1116. · Zbl 0389.47030 [2] Haraux, A., Weissler, F.B.. «Non-uniqueness for a semi-linear initial value problem». Indiana University Mathematics Journal, vol. 31, n° 2, (1982), p. 167-189. · Zbl 0465.35049 [3] Haraux, A., Kirane, M.. «Estimations C1 pour des problèmes paraboliques semi-linéaires». Université Pierre et Marie Curie. ParisV. · Zbl 0494.35054 [4] Weissler, F.B.. «Local existence and non-existence for semilinear parabolic equations in Lp». Indiana University Mathematics Journal, vol. 29, n° 1, (1980), p. 79-102. · Zbl 0443.35034 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.