Backward uniqueness for solutions of linear parabolic equations
Igor Kukavica · Proceedings of the American Mathematical Society · 2003
We address the backward uniqueness property for the equation u t − Δ u = w j ∂ j u + v u u_t-\Delta u = w_j\partial _{j}u+v u in R n × ( T 0 , 0 ] {\mathbb R}^n\times (T_0,0] . We show that under rather general conditions on v v and w w , u | t = 0 = 0 u|_{t=0}=0 implies that u u vanishes to infinite order for all points ( x , 0 ) (x,0) . It follows that the backward uniqueness holds if w = 0 w=0 and v ∈ L ∞ ( [ 0 , T 0 ] , L p ( R