We prove for some singular initial data the existence of a solution u(t)=u(t)+v(t) ε C([0,T]:L3(ø3)) of the nonlinear heat equation with nonlinearity u3, which is not equal to Weissler's solution. The proof lies on the study of the perturbed equation on v(t) in weak-L6.
Sur la non-unicite des solutions faibles de l'equation de la chaleur non lineaire avec non-linearite u^3 / E. Terraneo. - In: COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE. - ISSN 0764-4442. - 328:9(1999 May), pp. 759-762. [10.1016/S0764-4442(99)80267-5]
Sur la non-unicite des solutions faibles de l'equation de la chaleur non lineaire avec non-linearite u^3
E. TerraneoPrimo
1999
Abstract
We prove for some singular initial data the existence of a solution u(t)=u(t)+v(t) ε C([0,T]:L3(ø3)) of the nonlinear heat equation with nonlinearity u3, which is not equal to Weissler's solution. The proof lies on the study of the perturbed equation on v(t) in weak-L6.
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