Analysis of a Hydrodynamic Thermoelastic Mixture Model

[2408.06733] Analysis of a Hydrodynamic Thermoelastic Mixture Model Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Analysis of PDEs arXiv:2408.06733 (math) [Submitted on 13 Aug 2024 ( v1 ), last revised 14 Aug 2026 (this version, v3)] Title: Analysis of a Hydrodynamic Thermoelastic Mixture Model Authors: Michael Eden , Meraj Alam , Prakash Kumar , G P Raja Sekhar View a PDF of the paper titled Analysis of a Hydrodynamic Thermoelastic Mixture Model, by Michael Eden and 3 other authors View PDF HTML (experimental) Abstract: This study proposes and explores a hydrodynamic thermo-elasticity system within the context of mixture models, encompassing fluid and solid phases, with particular emphasis on biological tissues and tumor-related phenomena. While tumor growth dynamics are not explicitly modeled yet, this work examines the interaction between thermal effects and hydrodynamics on short-time scales where the tumor size typically remains stable. We establish the existence of a unique weak solution within the framework of implicit evolution equations where we exploit the intricate coupling mechanisms inherent to the PDE system. To further investigate the model, we then study the one-dimensional model and explore in detail the complex interplay between fluid flow, solid deformation, and heat transfer. This complex coupled system of equations is then reduced over a short time scale to obtain semi-analytical solutions. Comments: Updated and reworked the analysis section, Subjects: Analysis of PDEs (math.AP) MSC classes: 74E30, 74F05, 74F10, 35M30 Cite as: arXiv:2408.06733 [math.AP] (or arXiv:2408.06733v3 [math.AP] for this version) https://doi.org/10.48550/arXiv.2408.06733 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Michael Eden [ view email ] [v1] Tue, 13 Aug 2024 08:49:01 UTC (3,443 KB) [v2] Mon, 10 Feb 2025 16:18:08 UTC (3,475 KB) [v3] Fri, 14 Aug 2026 23:43:42 UTC (451 KB) Full-text links: Access Paper: View a PDF of the paper titled Analysis of a Hydrodynamic Thermoelastic Mixture Model, by Michael Eden and 3 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.AP < prev | next > new | recent | 2024-08 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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