A Deterministic Optimal Design Problem for the Heat Equation
نویسندگان
چکیده
For the heat equation on a bounded subdomain Ω of R, we investigate the optimal shape and location of the observation domain in observability inequalities. A new decomposition of L(R) into heat packets allows us to remove the randomization procedure and assumptions on the geometry of Ω in previous works. The explicit nature of the heat packets gives new information about the observability constant in the inverse problem.
منابع مشابه
The Optimal Design of Heat Sinks: A Review
Heat sinks are used in industrial equipment to dissipate the excess heat from their heat-generating parts to the ambient. In the last few years, efforts on manufacturing electronic or mechanical devices with less weight, space, and lower cost were spent. Heat dissipation from the heat sink is stalling a big problem which many researchers are trying to solve. The aim of this study is to brief th...
متن کاملDeveloping a New Algorithm for a Utility-based Network Design Problem with Elastic Demand
Developing the infrastructures for preventing non-communicable diseases is one of the most important goals of healthcare context in recent years. In this regard, the number and capacity of preventive healthcare facilities as well as assignment of customers to facilities should be determined for each region. Besides the accessibility, the utility of customers is a determinative factor in partici...
متن کاملFinding the Optimal Place of Sensors for a 3-D Damped Wave Equation by using Measure Approach
In this paper, we model and solve the problem of optimal shaping and placing to put sensors for a 3-D wave equation with constant damping in a bounded open connected subset of 3-dimensional space. The place of sensor is modeled by a subdomain of this region of a given measure. By using an approach based on the embedding process, first, the system is formulated in variational form;...
متن کاملAdaptive Unstructured Grid Generation Scheme for Solution of the Heat Equation
An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...
متن کاملConstrained Multi-Objective Optimization Problems in Mechanical Engineering Design Using Bees Algorithm
Many real-world search and optimization problems involve inequality and/or equality constraints and are thus posed as constrained optimization problems. In trying to solve constrained optimization problems using classical optimization methods, this paper presents a Multi-Objective Bees Algorithm (MOBA) for solving the multi-objective optimal of mechanical engineering problems design. In the pre...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Control and Optimization
دوره 55 شماره
صفحات -
تاریخ انتشار 2017