Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model

Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Numerical approximation of the two-species Shigesada-Kawasaki-Teramoto model Ghufran A. Al-Musawi, Akil J. Harfash This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3166624/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract In this article, the finite element approximation of the two-species Shigesada-Kawasaki-Teramoto model, with cross-diffusion for one species, is studied. In the beginning, the regularized problem of the model and the entropy proof of the regularized problem were presented. Also, an approxi- mation of the regularized problem using the finite element method was introduced. A number of bounds were found in different spaces for approximate solutions. In addition, depending on the bounds that are obtained, the convergence of the approximate problem to the weak form of the problem was studied, and thus the existence of solutions to the Shigesada-Kawasaki-Teramoto model was proved. Also, a practical algorithm for solving the approximate problem was presented and used to calculate the numerical results of the problem. Galerkin finite element cross-diffusion convergence Shigesada-Kawasaki-Teramoto. Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3166624","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":218553428,"identity":"1a6800c5-ff9c-45ee-a7ab-22397ee9b224","order_by":0,"name":"Ghufran A. Al-Musawi","email":"","orcid":"","institution":"University of Basrah","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Ghufran","middleName":"A.","lastName":"Al-Musawi","suffix":""},{"id":218553429,"identity":"b2f7db9c-780c-4e3c-8494-a6cba4f9f2b0","order_by":1,"name":"Akil J. 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