A Free Boundary Problem for an Elliptic–Parabolic System: Application to a Model of Tumor Growth

DOI10.1081/PDE-120020486zbMath1031.35151OpenAlexW1979364234MaRDI QIDQ4807597

Avner Friedman, Borys V. Bazaliy

Publication date: 19 May 2003

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1081/pde-120020486

zbMATH Keywords

existencetumor growthuniquenesselliptic variational inequalityelliptic-parabolic system

Mathematics Subject Classification ID

Related Items (42)

Classical solutions of many-dimensional elliptic-parabolic free boundary problems ⋮ Bifurcation for a free boundary problem with surface tension modeling the growth of multi-layer tumors ⋮ Tumor growth towards lower extracellular matrix conductivity regions under Darcy's law and steady morphology ⋮ A hyperbolic free boundary problem modeling tumor growth: Asymptotic behavior ⋮ Continuation along bifurcation branches for a tumor model with a necrotic core ⋮ Bifurcation for a free boundary problem modeling the growth of tumors with a drug induced nonlinear proliferation rate ⋮ Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors ⋮ Linear Stability Analysis for a Free Boundary Problem Modeling Multilayer Tumor Growth with Time Delay ⋮ Symmetry-breaking bifurcation for a free-boundary tumor model with time delay ⋮ The linear stability for a free boundary problem modeling multilayer tumor growth with time delay ⋮ Regularity of solutions to a free boundary problem modeling tumor growth by Stokes equation ⋮ Fictitious domains and level sets for moving boundary problems. Applications to the numerical simulation of tumor growth ⋮ A three-dimensional steady-state tumor system ⋮ Florin-type problem for the parabolic equation with power nonlinearity ⋮ A model of controlled growth ⋮ Asymptotic Behaviour of Solutions of a Multidimensional Moving Boundary Problem Modeling Tumor Growth ⋮ The Muskat problem with surface tension and a nonregular initial interface ⋮ A Cahn--Hilliard Model for Cell Motility ⋮ Stability and instability of Liapunov-Schmidt and Hopf bifurcation for a free boundary problem arising in a tumor model ⋮ On the blow-up mechanism of moving boundary problems ⋮ Well-posedness and stability of a free boundary problem modeling the growth of multi-layer tumors ⋮ MATHEMATICAL ANALYSIS AND CHALLENGES ARISING FROM MODELS OF TUMOR GROWTH ⋮ Bifurcation for a free boundary problem modeling the growth of multi-layer tumors ⋮ Bifurcation from stability to instability for a free boundary problem arising in a tumor model ⋮ Asymptotic stability for a free boundary problem arising in a tumor model ⋮ Analyticity of solutions to a free boundary problem modeling the growth of multi-layer tumors ⋮ Hölder space solutions of free boundary problems that arise in combustion theory ⋮ On the justification of the quasistationary approximation of several parabolic moving boundary problems. Part I ⋮ Bifurcation for a free boundary problem modeling tumor growth with inhibitors ⋮ Free boundary problems with surface tension conditions ⋮ The impact of time delay in a tumor model ⋮ Well-posedness and stability of a multi-dimensional tumor growth model ⋮ Lie group action and stability analysis of stationary solutions for a free boundary problem modelling tumor growth ⋮ Analysis of an elliptic-parabolic free boundary problem modelling the growth of non-necrotic tumor cord ⋮ On a free boundary problem for the relaxation transfer equation ⋮ Bifurcations for a multidimensional free boundary problem modeling the growth of tumor cord ⋮ Problem with free boundary for systems of equations of reaction-diffusion type ⋮ The Hele-Shaw problem with surface tension in a half-plane: a model problem ⋮ The Hele-Shaw problem with surface tension in a half-plane ⋮ Asymptotic analysis of a mathematical model of the atherosclerosis development ⋮ Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations and Schauder's estimates for a degenerate parabolic problem with dynamic boundary conditions ⋮ Optimal control oriented to therapy for a free-boundary tumor growth model

Cites Work

• Unnamed Item
• The Hele--Shaw problem and area-preserving curve-shortening motions
• Classical solutions of the Stefan problem
• Analysis of a mathematical model for the growth of tumors
• Growth of necrotic tumors in the presence and absence of inhibitors
• Symmetry-breaking bifurcation of analytic solutions to free boundary problems: An application to a model of tumor growth
• Classical Solutions of Multidimensional Hele--Shaw Models
• Stefan problem for the laplace equation with regard for the curvature of the free boundary

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