{"title":"新经济地理学中的平流-扩散模式形成","authors":"Kensuke Ohtake","doi":"arxiv-2407.05804","DOIUrl":null,"url":null,"abstract":"A new economic geography model is proposed in which the migration of mobile\nworkers is proximate and perturbed by non-economic factors. The model consists\nof a tractable core-periphery model assuming a quasi-linear log utility\nfunction of consumers and an advection-diffusion equation governing the time\nevolution of a population distribution. The stability of a spatially\nhomogeneous stationary solution and the large time behavior of solutions to the\nmodel on a one-dimensional periodic space are investigated. When the spatially\nhomogeneous stationary solution is unstable, solutions starting around it are\nfound to eventually form spatial patterns with several urban areas in which\nmobile workers agglomerate.","PeriodicalId":501188,"journal":{"name":"arXiv - ECON - Theoretical Economics","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pattern formation by advection-diffusion in new economic geography\",\"authors\":\"Kensuke Ohtake\",\"doi\":\"arxiv-2407.05804\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A new economic geography model is proposed in which the migration of mobile\\nworkers is proximate and perturbed by non-economic factors. The model consists\\nof a tractable core-periphery model assuming a quasi-linear log utility\\nfunction of consumers and an advection-diffusion equation governing the time\\nevolution of a population distribution. The stability of a spatially\\nhomogeneous stationary solution and the large time behavior of solutions to the\\nmodel on a one-dimensional periodic space are investigated. When the spatially\\nhomogeneous stationary solution is unstable, solutions starting around it are\\nfound to eventually form spatial patterns with several urban areas in which\\nmobile workers agglomerate.\",\"PeriodicalId\":501188,\"journal\":{\"name\":\"arXiv - ECON - Theoretical Economics\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - ECON - Theoretical Economics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2407.05804\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - ECON - Theoretical Economics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.05804","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Pattern formation by advection-diffusion in new economic geography
A new economic geography model is proposed in which the migration of mobile
workers is proximate and perturbed by non-economic factors. The model consists
of a tractable core-periphery model assuming a quasi-linear log utility
function of consumers and an advection-diffusion equation governing the time
evolution of a population distribution. The stability of a spatially
homogeneous stationary solution and the large time behavior of solutions to the
model on a one-dimensional periodic space are investigated. When the spatially
homogeneous stationary solution is unstable, solutions starting around it are
found to eventually form spatial patterns with several urban areas in which
mobile workers agglomerate.
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