Modelling and predicting coastal zone depth profile evolution: a survey

Denis Baramiya, Mikhail Lavrentiev, Renato Spigler
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Abstract

Abstract We survey results concerning the problem of identifying depth profiles at coastal zone, which evolve in time due to natural as well as anthropic activities. This issue is relevant to control the modifications of the environment occurring near sea coastlines, but also in river's estuaries and harbors. One of the main goals is to predict the time evolution of the depth profile in the long-term (i.e., over years or decades, say), and to do this on the basis of real observed and measured data , available in several databases. Most mathematical models are formulated in terms of partial differential equations of the diffusive type, in one or two space dimensions. Consequently, from the mathematical standpoint, the aforementioned identification problem takes on the form of an inverse problem for some given parabolic equation associated with suitable initial and boundary conditions.
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海岸带深度剖面演化模拟与预测综述
摘要本文调查了受自然和人为活动影响而随时间变化的海岸带深度剖面识别问题。这个问题不仅关系到控制发生在海岸线附近的环境变化,而且关系到河流的河口和港口。主要目标之一是预测深度剖面的长期(例如,几年或几十年)的时间演变,并在几个数据库中可用的实际观测和测量数据的基础上进行预测。大多数数学模型是用扩散型偏微分方程在一个或两个空间维度上表述的。因此,从数学的角度来看,上述识别问题对某些给定的具有适当初始条件和边界条件的抛物方程具有反问题的形式。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
3
审稿时长
16 weeks
期刊介绍: Communications in Applied and Industrial Mathematics (CAIM) is one of the official journals of the Italian Society for Applied and Industrial Mathematics (SIMAI). Providing immediate open access to original, unpublished high quality contributions, CAIM is devoted to timely report on ongoing original research work, new interdisciplinary subjects, and new developments. The journal focuses on the applications of mathematics to the solution of problems in industry, technology, environment, cultural heritage, and natural sciences, with a special emphasis on new and interesting mathematical ideas relevant to these fields of application . Encouraging novel cross-disciplinary approaches to mathematical research, CAIM aims to provide an ideal platform for scientists who cooperate in different fields including pure and applied mathematics, computer science, engineering, physics, chemistry, biology, medicine and to link scientist with professionals active in industry, research centres, academia or in the public sector. Coverage includes research articles describing new analytical or numerical methods, descriptions of modelling approaches, simulations for more accurate predictions or experimental observations of complex phenomena, verification/validation of numerical and experimental methods; invited or submitted reviews and perspectives concerning mathematical techniques in relation to applications, and and fields in which new problems have arisen for which mathematical models and techniques are not yet available.
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