, However, in our final result, we prefer to exploit Proposition 6.6 to provide an alternative, more direct argument. all C with ?T ?1 ? |C| ? ?T ?1 , the constant state C is not attainable at time T for problem
, It is enough to apply Proposition 6.6 to establish thatK ?,? ? NA L 2 ,box 1 , and then apply
, We do not pursue the goal of stating futher and finer results with ad hoc choices of K in the setting of Theorem 6.7. Interested readers can infer such results from Proposition 6.6, and even go futher using the ideas and auxiliary results
, Let us underline that this property holds true for sufficiently regular weak solutions of (Pb box ), with (?, 1 ? ?) × (?, T ? ?) replaced by (?, 1 ? ?) × (?, T )
, 1))) regularity and the representation (5.22) with monotone functions y(·, t) -extends to solutions of the viscous Burgers equation
, Acknowledgement The publication has been prepared with the support of the RUDN University Program 5-100. The work in this paper was supported by the French ANR agency (project CoToCoLa No. ANR-11-JS01-006-01) and IFCAM project "Conservation Laws: BV s , Control, Interfaces
, Panov for useful discussions on matters related to the material of Section 5. S. S. G would like to thank J-M. Coron for introducing him to the problem. The authors would like to thank GSSI (L'Aquila, Italy) as large part of the work was done during their stay
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