{"1012825ed1ef9d03d4f860e87a435b62mhartmann":{"DOI":"10.1002/mma.1133","ISBN":"","ISSN":"1099-1476","URL":"http://dx.doi.org/10.1002/mma.1133","abstract":"We investigate a reaction--diffusion system proposed by H. Meinhardt\n\tas a model for pattern formation on seashells. We give a new proof\n\tfor the existence of a local weak solution for general initial conditions\n\tand parameters upon using an iterative approach. Furthermore, the\n\tsolution is shown to exist globally for suitable initial data. The\n\tbehavior of the solution in time and space is illustrated through\n\tnumerical simulations. Copyright � 2009 John Wiley & Sons, Ltd.","annote":"","author":[{"family":"Kelkel","given":"Jan"},{"family":"Surulescu","given":"Christina"}],"citation-label":"kelkel2009solution","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Mathematical Methods in the Applied Sciences","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2009"]],"literal":"2009"},"event-place":"","id":"1012825ed1ef9d03d4f860e87a435b62mhartmann","interhash":"238011336a3e7e95eec6ac89a22367c8","intrahash":"1012825ed1ef9d03d4f860e87a435b62","issue":"17","issued":{"date-parts":[["2009"]],"literal":"2009"},"keyword":"equations, formation, global pattern reaction--diffusion solution vorlaeufig weak","misc":{"issn":"1099-1476","doi":"10.1002/mma.1133"},"note":"","number":"17","number-of-pages":"19","page":"2267--2286","page-first":"2267","publisher":"John Wiley & Sons, Ltd.","publisher-place":"","status":"","title":"A weak solution approach to a reaction--diffusion system modeling\n\tpattern formation on seashells","type":"article-journal","username":"mhartmann","version":"","volume":"32"},"3db799e086f892c66bf169c998bee007mhartmann":{"DOI":"10.1007/s00285-009-0284-5","ISBN":"","ISSN":"0303-6812","URL":"http://dx.doi.org/10.1007/s00285-009-0284-5","abstract":"","annote":"","author":[{"family":"Kelkel","given":"Jan"},{"family":"Surulescu","given":"Christina"}],"citation-label":"kelkel2010stochastic","collection-editor":[],"collection-title":"","container-author":[],"container-title":"Journal of Mathematical Biology","documents":[],"edition":"","editor":[],"event-date":{"date-parts":[["2010"]],"literal":"2010"},"event-place":"","id":"3db799e086f892c66bf169c998bee007mhartmann","interhash":"6b30ed3e0c1494d385b7856c79f8ee1c","intrahash":"3db799e086f892c66bf169c998bee007","issue":"6","issued":{"date-parts":[["2010"]],"literal":"2010"},"keyword":"35K57, 60H15, 92C15 Pattern Stochastic equations, formation, reaction--diffusion vorlaeufig","misc":{"issn":"0303-6812","language":"English","doi":"10.1007/s00285-009-0284-5"},"note":"","number":"6","number-of-pages":"31","page":"765--796","page-first":"765","publisher":"Springer-Verlag","publisher-place":"","status":"","title":"On a stochastic reaction--diffusion system modeling pattern formation\n\ton seashells","type":"article-journal","username":"mhartmann","version":"","volume":"60"}}