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Nonuniqueness of bounded solutions for some BV outside a hyperplane vector field. (Non unicité des solutions bornées pour un champ de vecteurs BV en dehors d’un hyperplan.) (French) Zbl 1024.35029
Summary: We present here an example of a plane time-dependent bounded divergence-free vector field and a bounded non-zero solution of the homogeneous Cauchy problem for the associated transport equation.

35F10 Initial value problems for linear first-order PDEs
Full Text: DOI
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