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Control Signals Syst."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Turnpike results hold a central position in the area of applied mathematics, offering profound insights into the long-time behavior of optimal control systems. They play an important role in guiding decision-making processes in dynamic systems. Often dynamic systems depend on uncertain data and\/or parameters. In this paper, optimal boundary control problems for the transport equation with random initial data and random source term are considered. The paper begins with the numerical analysis of the turnpike phenomenon for an optimal boundary control problem with nonlinear time-varying feedback control, where the initial data are perturbed by randomized Fourier series and the source term is perturbed by a random variable. Further, an integral turnpike result is presented for the optimal controls and the corresponding optimal states of an optimal boundary control problem with random initial data. A turnpike result is also presented for an optimal boundary control problem governed by a transport equation with random source term, where optimal control, optimal expected state, and variance satisfy an integral turnpike inequality. The turnpike constant, the expected value, and the variance are further specified for Gaussian and uniformly distributed random variables.<\/jats:p>","DOI":"10.1007\/s00498-025-00422-y","type":"journal-article","created":{"date-parts":[[2025,8,25]],"date-time":"2025-08-25T06:32:36Z","timestamp":1756103556000},"page":"969-1006","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A turnpike result for boundary control problems governed by the transport equation under uncertainty"],"prefix":"10.1007","volume":"37","author":[{"given":"Noboru","family":"Sakamoto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael","family":"Schuster","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,8,25]]},"reference":[{"key":"422_CR1","volume-title":"Linear programming and economic analysis","author":"R Dorfmann","year":"1958","unstructured":"Dorfmann R, Samuelson PA, Solow R (1958) Linear programming and economic analysis. 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