Zero-noise solutions of linear transport equations without uniqueness: an example |
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Authors: | Stefano Attanasio Franco Flandoli |
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Institution: | 1. Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy;2. Dipartimento di Matematica Applicata “U. Dini”, Università di Pisa, Via Buonarroti 1, 56127 Pisa, Italy |
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Abstract: | We consider a classical one-dimensional example of linear transport equation without uniqueness of weak solutions. Under a suitable multiplicative noise perturbation, the equation is well posed. We identify the two solutions of the deterministic equation obtained in the zero-noise limit. In addition, we prove that the zero-viscosity solution exists and is different from them. To cite this article: S. Attanasio, F. Flandoli, C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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