Gevrey regularity of solutions of evolution equations and boundary controllability [microform]
- Bib ID:
- 3283090
- Format:
- Book and Microform
- Author:
- Taylor, Stephen William
- Description:
- 182 p.
- Summary:
-
Chapters 1 to 4 of this work generalize the work of Littman and Markus (17) on the 'Exact Boundary Controllability of a Hybrid System of Elasticity'. Chapter 5 is independent of the earlier chapters and it deals with the Gevrey regularity of strongly continuous semigroups. In Chapter 1, we consider equations of the form$$\rm{\partial\sp2w\over\partial t\sp2}(x{,}t)+\sum\limits\sbsp{i=0}{4} a\sb{i}(x){\partial\sp{i}w\over\partial x\sp{i}}(x{,}t) + \sum\limits\sbsp{i=0}{2} b\sb{i}(x){\partial\sp{i+1}w\over\partial x\sp{i}\partial t}(x{,}t)=0,$
In Chapter 2, we restrict the coefficients to be constants and show that in this case we obtain solutions which are analytic functions of t for t $>$ 0. In Chapter 3, we use the Gevrey regularity established in Chapter 1 to obtain solutions which vanish for t $>$ T (T being a given positive constant). In fact, we consider more general equations which are assumed to satisfy results similar to those proved in Chapter 1 and which have coefficients possessing a 'Gevrey' dependence on time. We need the Gevrey regularity to solve the equations in the 'x-direction'. We apply the theory of the previous chapters in Chapter 4. Here, we consider the boundary controllability of a hybrid system consisting of an elastic beam clamped at one end to a space shuttle and at the other end to an antenna. The beam equation has variable coefficients and the ordinary differential equation of motion for the antenna yields unusual boundary conditions.
We prove that the system is exactly controllable with two open loop controllers applied only to the antenna and that the rest state may be reached during an arbitrarily short time duration. The case in which the shuttle is rotating is also considered. This generalizes the work in (17). The Gevrey regularity of semigroups is dealt with in Chapter 5. We develop theorems yielding both necessary and sufficient conditions for this regularity, which is a property falling naturally between those of differentiability and analyticity of semigroups.
- Notes:
-
- (UnM)AAI9008301
- Source: Dissertation Abstracts International, Volume: 50-11, Section: B, page: 5110.
- Thesis (Ph.D.)--University of Minnesota, 1989.
- Reproduction:
- Microfiche. Ann Arbor, Mich.: University Microfilms International.
- Subject:
- Mathematics
- Other authors/contributors:
- University of Minnesota
- Copyright:
-
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Copyright status was determined using the following information:
- Material type:
- Literary Dramatic Musical
- Published status:
- Unpublished
- Creation date:
- 1989
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