natural vibration analysis of plates represents an important issue in engineering applications. in this paper, a new and simplify method for vibration analysis of circular and rectangular plates is presented. the design of an effective robust controller, which consistently attenuates transverse vibration of the plate caused by an external disturbance force, is given. the dynamics of the plate i...

Following the recent analysis of Lucas and Rossi-Hansberg [10], we study the equilibrium structure of cities. By adopting a different (monetary) specification of commuting costs, we are able to prove the existence of equilibrium in more general situations: non-circular cities, or multi-sectorial production. The main mathematical tool in this paper is the use of optimal transportation theory. Th...

Urban areas are complex systems, comprising many interacting infrastructure sectors. Understanding these inter-relationships is essential to sustainable urban and infrastructure development. Research focused on single sectors, or over limited timescales, will inevitably fail to capture these interdependencies and dynamics. Consequently this project is carrying out work to investigate these sect...

We prove the trace-norm convergence of the Trotter product formula for nonself-adjoint Gibbs semigroups. For any m-sectorial generators A and B such that e ?tRe A is in the trace-class for t > 0, the Trotter product formula converges in the trace-norm. With smallness conditions on B with respect to A, we give error bound estimates of the convergence rate in this topology.

We study the numerical solution of semilinear parabolic PDEs on unbounded spatial domains in R2 whose solutions blow up in finite time. Of particular interest are the cases where = R2 or is a sectorial domain in R2. We derive the nonlinear absorbing boundary conditions for corresponding, suitably chosen computational domains and then employ a simple adaptive time-stepping scheme to compute the ...