{"product_id":"modelling-and-analysis-of-nonnecrotic-tumors-a-functional-analytic-approach-von-anca-voichita-matioc","title":"Modelling and analysis of nonnecrotic tumors","description":"\u003cp\u003eModelling and simulation of tumor growth is one of the challenging frontiers of applied mathematics. We study in this work a mathematical model for the growth of nonnecrotic tumors in different regimes of vascularisation. The tumor is treated as an incompressible fluid, tissue elasticity is neglected, and the mathematical model is a moving boundary problem. In the radially symmetric case we establish the existence of a unique radially symmetric stationary solution and show, that if the initial tumor is radially symmetric, there exists a unique radially symmetric solution of the problem, which exists for all times. The asymptotic behaviour of this solution it is also discussed. If we consider star-shaped initial tumor domains, we can re-express the mathematical model as an abstract evolution equation. Using general results for parabolic equations we prove the well-posedness of the model. The stability properties of the radially symmetric equilibrium are studied using the principle of linearised stability . Finally, we show, via a bifurcation argument, that there exist also other stationary solutions of the problem, which are no longer radially symmetric.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838113241\"\u003e\u003ch3\u003eA Functional Analytic Approach\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783838113241","offer_id":39456804601949,"sku":"9783838113241","price":69.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/6bc4d3c6-8544-4d15-8930-e27a65470b1a.jpg?v=1776320439","url":"https:\/\/shop.autorenwelt.de\/products\/modelling-and-analysis-of-nonnecrotic-tumors-a-functional-analytic-approach-von-anca-voichita-matioc","provider":"Autorenwelt Shop","version":"1.0","type":"link"}