{"date_updated":"2025-12-19T11:03:57Z","intvolume":"        29","date_created":"2025-12-19T11:03:50Z","volume":29,"type":"journal_article","publication_identifier":{"issn":["0956-7925","1469-4425"]},"status":"public","author":[{"first_name":"T.","last_name":"HILLEN","full_name":"HILLEN, T."},{"last_name":"PAINTER","full_name":"PAINTER, K. J.","first_name":"K. J."},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael","id":"31496"}],"doi":"10.1017/s0956792517000328","publication_status":"published","language":[{"iso":"eng"}],"abstract":[{"text":"<jats:p>Adhesion between cells and other cells (cell–cell adhesion) or other tissue components (cell–matrix adhesion) is an intrinsically non-local phenomenon. Consequently, a number of recently developed mathematical models for cell adhesion have taken the form of non-local partial differential equations, where the non-local term arises inside a spatial derivative. The mathematical properties of such a non-local gradient term are not yet well understood. Here we use sophisticated estimation techniques to show local and global existence of classical solutions for such examples of adhesion-type models, and we provide a uniform upper bound for the solutions. Further, we discuss the significance of these results to applications in cell sorting and in cancer invasion and support the theoretical results through numerical simulations.</jats:p>","lang":"eng"}],"issue":"4","user_id":"31496","publisher":"Cambridge University Press (CUP)","publication":"European Journal of Applied Mathematics","citation":{"short":"T. HILLEN, K.J. PAINTER, M. Winkler, European Journal of Applied Mathematics 29 (2017) 645–684.","chicago":"HILLEN, T., K. J. PAINTER, and Michael Winkler. “Global Solvability and Explicit Bounds for Non-Local Adhesion Models.” <i>European Journal of Applied Mathematics</i> 29, no. 4 (2017): 645–84. <a href=\"https://doi.org/10.1017/s0956792517000328\">https://doi.org/10.1017/s0956792517000328</a>.","apa":"HILLEN, T., PAINTER, K. J., &#38; Winkler, M. (2017). Global solvability and explicit bounds for non-local adhesion models. <i>European Journal of Applied Mathematics</i>, <i>29</i>(4), 645–684. <a href=\"https://doi.org/10.1017/s0956792517000328\">https://doi.org/10.1017/s0956792517000328</a>","ama":"HILLEN T, PAINTER KJ, Winkler M. Global solvability and explicit bounds for non-local adhesion models. <i>European Journal of Applied Mathematics</i>. 2017;29(4):645-684. doi:<a href=\"https://doi.org/10.1017/s0956792517000328\">10.1017/s0956792517000328</a>","mla":"HILLEN, T., et al. “Global Solvability and Explicit Bounds for Non-Local Adhesion Models.” <i>European Journal of Applied Mathematics</i>, vol. 29, no. 4, Cambridge University Press (CUP), 2017, pp. 645–84, doi:<a href=\"https://doi.org/10.1017/s0956792517000328\">10.1017/s0956792517000328</a>.","ieee":"T. HILLEN, K. J. PAINTER, and M. Winkler, “Global solvability and explicit bounds for non-local adhesion models,” <i>European Journal of Applied Mathematics</i>, vol. 29, no. 4, pp. 645–684, 2017, doi: <a href=\"https://doi.org/10.1017/s0956792517000328\">10.1017/s0956792517000328</a>.","bibtex":"@article{HILLEN_PAINTER_Winkler_2017, title={Global solvability and explicit bounds for non-local adhesion models}, volume={29}, DOI={<a href=\"https://doi.org/10.1017/s0956792517000328\">10.1017/s0956792517000328</a>}, number={4}, journal={European Journal of Applied Mathematics}, publisher={Cambridge University Press (CUP)}, author={HILLEN, T. and PAINTER, K. J. and Winkler, Michael}, year={2017}, pages={645–684} }"},"title":"Global solvability and explicit bounds for non-local adhesion models","_id":"63371","year":"2017","page":"645-684"}