Sentence examples for a unique continuation from inspiring English sources

This is called a unique continuation theorem (we note the analog fails for hyperbolic equations).

So, from [13, Theorem ] and a unique continuation argument we obtain that in.

We prove a unique continuation from infinity theorem for regular waves of the form [□+V t,x)]ϕ="0.

This result however relies on a unique continuation theorem by Tataru [194] and it is unlikely to provide Hölder type of stability estimate as above.

The aim of this article, is to present a unique continuation result for solutions of a differential inequalities of the form: ‖ P ( x, D ) u ( x ) ‖ E ≤ ‖ V ( x ) u ( x ) ‖ E, (1).

As a consequence of the null controllability, we obtain the observability estimate for backward stochastic heat equations, which leads to a unique continuation property for backward stochastic heat equations, and hence the desired approximate controllability for forward stochastic heat equations.

In this paper, we established a quantitative unique continuation results for a coupled heat equations, with the homogeneous Dirichlet boundary condition, on a bounded convex domain Ω of (mathbb{R}^{d}) with smooth boundary ∂Ω.

We prove a strong unique continuation result for Schrödinger inequalities, i.e., we obtain that a flat u so that |Δu| ≤|Vu| should be zero, provided that V is a radial Kato potential.

The approximate controllability of the unperturbed linear system is described by a quantitative unique continuation property for trajectories of the system dual to the unperturbed one.

The following corollary may be viewed as an abstract unique continuation result.

The first '⩽' in (1.2) describes a certain quantitative unique continuation property of solutions to the evolution equation mathbf{z}'(t)=-A^mathbf{z}(t quad mbox{for }tin[0,T). This property implies, in particular, that the unperturbed linear system ((1.1) with (mathbf{f}equiv0 )) is approximately controllable in time T; see Lemma 3.2 and also [2], Theorem 11.2.1.