ترغب بنشر مسار تعليمي؟ اضغط هنا

Unique continuation property with partial information for two-dimensional anisotropic elasticity systems

76   0   0.0 ( 0 )
 نشر من قبل Yikan Liu
 تاريخ النشر 2019
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we establish a novel unique continuation property for two-dimensional anisotropic elasticity systems with partial information. More precisely, given a homogeneous elasticity system in a domain, we investigate the unique continuation by assuming only the vanishing of one component of the solution in a subdomain. Using the corresponding Riemann function, we prove that the solution vanishes in the whole domain provided that the other component vanishes at one point up to its second derivatives. Further, we construct several examples showing the possibility of further reducing the additional information of the other component. This result possesses remarkable significance in both theoretical and practical aspects because the required data is almost halved for the unique determination of the whole solution.



قيم البحث

اقرأ أيضاً

136 - N. Honda , C.-L. Lin , G. Nakamura 2015
This paper concerns about the weak unique continuation property of solutions of a general system of differential equation/inequality with a second order strongly elliptic system as its leading part. We put not only some natural assumption which calle d {sl basic assumptions}, but also some technical assumptions which we called {sl further assumptions}. It is shown as usual by first applying the Holmgren transform to this inequality and then establishing a Carleman estimate for the leading part of the transformed inequality. The Carleman estimate given via a partition of unity and Carleman estimate for the operator with constant coefficients obtained by freezing the coefficients of the transformed leading part at a point. A little more details about this are as follows. Factorize this operator with constant coefficients into two first order differential operators. Conjugate each factor by a Carleman weight and derive an estimate which is uniform with respect to the point at which we froze the coefficients for each conjugated factor by constructing a parametrix for its adjoint operator.
In this paper we prove a quantitative form of the strong unique continuation property for the Lame system when the Lame coefficients $mu$ is Lipschitz and $lambda$ is essentially bounded in dimension $nge 2$. This result is an improvement of our earl ier result cite{lin5} in which both $mu$ and $lambda$ were assumed to be Lipschitz.
We prove unique continuation properties for solutions of the evolution Schrodinger equation with time dependent potentials. As an application of our method we also obtain results concerning the possible concentration profiles of blow up solutions and the possible profiles of the traveling waves solutions of semi-linear Schrodinger equations.
108 - Hans Christianson 2013
We prove a strong conditional unique continuation estimate for irreducible quasimodes in rotationally invariant neighbourhoods on compact surfaces of revolution. The estimate states that Laplace quasimodes which cannot be decomposed as a sum of other quasimodes have $L^2$ mass bounded below by $C_epsilon lambda^{-1 - epsilon}$ for any $epsilon>0$ on any open rotationally invariant neighbourhood which meets the semiclassical wavefront set of the quasimode. For an analytic manifold, we conclude the same estimate with a lower bound of $C_delta lambda^{-1 + delta}$ for some fixed $delta>0$.
It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also decays exponentially at a later time. In particular, a strong solutio n of the Cauchy problem with compact initial profile can not be compactly supported at any later time unless it is the zero solution.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا