In this paper, we study certain unique continuation properties for solutions of the semilinear heat equation ∂tu−△u= g u), with the homogeneous Dirichlet boundary condition, over Ω× 0,T∗).
We introduce a new methodology for the numerical solution of Partial Differential Equations in general spatial domains: our algorithms are based on the use of the well-known Alternating Direction Implicit (ADI) approach in conjunction with a certain "Fourier continuation" (FC) method for the resolution of the Gibbs phenomenon.
A new PDE solver was introduced recently, in Part I of this two-paper sequence, on the basis of two main concepts: the well-known Alternating Direction Implicit (ADI) approach, on one hand, and a certain "Fourier Continuation" (FC) method for the resolution of the Gibbs phenomenon, on the other.
Previous to that, "therapeutic" abortions were allowed in certain circumstances where continuation of the pregnancy was life-threatening.
We cannot be certain that the continuation of the European crisis will push the North Atlantic into a double dip, but we can be fairly sure that, at best, the likelihood of a long Japanese-style malaise will rise markedly.
Unlike a complete teardown, these makeovers assume a certain level of continuation from the past.
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.
It is an ethos certain to see the continuation of publishing of the best young British novelists.
It isn't that far a stretch to suggest that under these circumstances advertisers might prove similarly enthusiastic about the continuation of certain shows even if broadcast or cable networks have lost interest.
The case of rickets illustrates the continuation of certain modalities of colonial tropical medicine: the same actors and institutions were involved, and the imperial networks that medicalized culture and race in the former colonies and the New Commonwealth came into play equally in conceptualizing immigrant and ethnic minority health needs at home.
