Energy-type estimates and global solvability in a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant

From MaRDI portal

Publication:2451888

Jump to:navigation, search

DOI10.1016/j.jde.2014.04.014zbMath1295.35144OpenAlexW2009746295MaRDI QIDQ2451888

Michael Winkler, Youshan Tao

Publication date: 26 May 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2014.04.014

zbMATH Keywords

energy estimates zero-flux boundary conditions logistic proliferation tissue remodeling elliptic-parabolic system coupled with an ODE first-order compatibility conditions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Reaction-diffusion equations (35K57) PDEs in connection with biology, chemistry and other natural sciences (35Q92) A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Cell movement (chemotaxis, etc.) (92C17)

Related Items

Global existence of classical solutions and numerical simulations of a cancer invasion model, Global existence of solutions to the chemotaxis system with logistic source under nonlinear Neumann boundary conditions, Uniform boundedness and eventual Hölder continuity to a cancer invasion model with remodeling of ECM and nonlinear diffusion, Some further progress for boundedness of solutions to a quasilinear higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion, Boundedness and asymptotic stabilization in a two-dimensional Keller–Segel–Navier–Stokes system with sub-logistic source, Boundedness in a logistic chemotaxis system with weakly singular sensitivity in dimension two, Global existence of a diffusive predator-prey model with prey-stage structure and prey-taxis, Boundedness in a two-dimensional two-species cancer invasion haptotaxis model without cell proliferation, A critical exponent for blow-up in a two-dimensional chemotaxis-consumption system, Asymptotic behaviour in a doubly haptotactic cross-diffusion model for oncolytic virotherapy, Blow-up prevention by sub-logistic sources in Keller-Segel cross diffusion type system, The vanishing viscosity limit on a model of Kareiva-Odell type in 2D, Boundedness of solutions to a chemotaxis-haptotaxis model with nonlocal terms, Global solvability and large time behavior in a two-species chemotaxis-consumption model, Convergence analysis from the indirect signal production to the direct one, Boundedness and large time behavior of solutions of a higher-dimensional haptotactic system modeling oncolytic virotherapy, Combined effects of nonlinear diffusion and gradient-dependent flux limitation on a chemotaxis-haptotaxis model, An interpolation inequality involving LlogL$L\log L$ spaces and application to the characterization of blow‐up behavior in a two‐dimensional Keller–Segel–Navier–Stokes system, Global weak solutions in a three-dimensional two-species cancer invasion haptotaxis model without cell proliferation, Global existence and uniform boundedness of smooth solutions to a parabolic-parabolic chemotaxis system with nonlinear diffusion, On a macrophage and tumor cell chemotaxis system with both paracrine and autocrine loops, Boundedness in a three-dimensional chemotaxis-haptotaxis model, Global boundedness in a fully parabolic attraction–repulsion chemotaxis model, Large Time Behavior in a Multidimensional Chemotaxis-Haptotaxis Model with Slow Signal Diffusion, A critical virus production rate for efficiency of oncolytic virotherapy, Does indirectness of signal production reduce the explosion-supporting potential in chemotaxis–haptotaxis systems? Global classical solvability in a class of models for cancer invasion (and more), Global solutions to a haptotaxis system with a potentially degenerate diffusion tensor in two and three dimensions, Finite-time blow-up and boundedness in a 2D Keller–Segel system with rotation, Global dynamics in a fully parabolic chemotaxis system with logistic source, Boundedness in a Keller-Segel system with external signal production, The small-convection limit in a two-dimensional chemotaxis-Navier-Stokes system, Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model, Global weak solution and boundedness in a three-dimensional competing chemotaxis, Finite time blow-up in the higher dimensional parabolic-elliptic-ODE minimal chemotaxis-haptotaxis system, Dampening effect of logistic source in a two-dimensional haptotaxis system with nonlinear zero-order interaction, Boundedness and large time behavior in a quasilinear chemotaxis model for tumor invasion, Boundedness in a two species attraction-repulsion chemotaxis system with two chemicals, Global existence and boundedness in a 2D Keller-Segel-Stokes system, Global well-posedness to a chemotaxis-Stokes system, Global classical solutions and convergence to a mathematical model for cancer cells invasion and metastatic spread, A note for global existence of a two-dimensional chemotaxis–haptotaxis model with remodeling of non-diffusible attractant, A chemotaxis-haptotaxis system with haptoattractant remodeling: boundedness enforced by mild saturation of signal production, Sub-logistic source can prevent blow-up in the 2D minimal Keller-Segel chemotaxis system, Blow-up prevention by logistic sources in a parabolic-elliptic Keller-Segel system with singular sensitivity, Tumor evolution models of phase-field type with nonlocal effects and angiogenesis, Boundedness in a two-species chemotaxis system with nonlinear resource consumption, Boundedness in a two-dimensional chemotaxis system with signal-dependent motility and logistic source, Global boundedness of weak solutions to a chemotaxis-haptotaxis model with \(p\)-Laplacian diffusion, Global classical solvability and stabilization in a two-dimensional chemotaxis–fluid system with sub-logarithmic sensitivity, Asymptotic behavior of a three-dimensional haptotactic cross-diffusion system modeling oncolytic virotherapy, A critical virus production rate for blow-up suppression in a haptotaxis model for oncolytic virotherapy, Global existence and boundedness of solutions to a two-species chemotaxis-competition system with singular sensitivity and indirect signal production, On the global existence of solutions to chemotaxis system for two populations in dimension two, On boundedness, blow-up and convergence in a two-species and two-stimuli chemotaxis system with/without loop, Global boundedness in an oncolytic virotherapy model with generalized logistic source, Boundedness and asymptotic behavior of solutions to a chemotaxis-haptotaxis model in high dimensions, Large time behavior of solutions to a fully parabolic chemotaxis-haptotaxis model in \(N\) dimensions, A new (and optimal) result for the boundedness of a solution of a quasilinear chemotaxis-haptotaxis model (with a logistic source), Boundedness and stabilization in a predator-prey model with prey-taxis and disease in predator species, Mathematical Research for Models Which is Related to Chemotaxis System, A Hybrid Multiscale Model for Cancer Invasion of the Extracellular Matrix, Mathematical modelling of cancer invasion: The multiple roles of TGF-β pathway on tumour proliferation and cell adhesion, A Stokes Two-Fluid Model for Cell Migration that Can Account for Physical Cues in the Microenvironment, Global boundedness in a three-dimensional chemotaxis-haptotaxis model, Critical mass on the Keller-Segel system with signal-dependent motility, Singular structure formation in a degenerate haptotaxis model involving myopic diffusion, Boundedness in a haptotactic cross-diffusion system modeling oncolytic virotherapy, Global solvability and large time behavior to a chemotaxis-haptotaxis model with nonlinear diffusion, Global boundedness of solutions to a chemotaxis–haptotaxis model with tissue remodeling, Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction, A study on time discretization and adaptive mesh refinement methods for the simulation of cancer invasion: the urokinase model, Global solvability and optimal control to a haptotaxis cancer invasion model with two cancer cell species, Boundedness of solutions for a quasilinear chemotaxis-haptotaxis model, Boundedness of solutions to a quasilinear higher-dimensional chemotaxis-haptotaxis model with nonlinear diffusion, Global solvability and boundedness to a coupled chemotaxis-fluid model with arbitrary porous medium diffusion, Global existence and eventual smoothness in a 2-D parabolic-elliptic system arising from ion transport networks, Global stability in a multi-dimensional predator-prey system with prey-taxis, Global boundedness in a two-competing-species chemotaxis system with two chemicals, Global existence and asymptotic stability in a competitive two-species chemotaxis system with two signals, Negligibility of haptotaxis effect in a chemotaxis–haptotaxis model, Global existence of a two-dimensional chemotaxis-haptotaxis model with remodeling of non-diffusible attractant, Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model, Boundedness of solutions to a quasilinear chemotaxis-haptotaxis model, Global boundedness of classical solutions to a two species cancer invasion haptotaxis model with tissue remodeling, Can fluid interaction influence the critical mass for taxis-driven blow-up in bounded planar domains?, Boundedness in a two-dimensional attraction-repulsion system with nonlinear diffusion, Global classical solutions to an oncolytic viral therapy model with triply haptotactic terms, Boundedness in a two-species chemotaxis system, The Keller-Segel system with logistic growth and signal-dependent motility, Analysis of a two-dimensional triply haptotactic model with a fusogenic oncolytic virus and syncytia, Solvability of solid tumor invasion model, Stabilization in a chemotaxis model for tumor invasion, Global classical solutions to a doubly haptotactic cross-diffusion system modeling oncolytic virotherapy, Boundedness and stabilization in a two-species chemotaxis system with two chemicals, Boundedness and stabilization in a two-species and two-stimuli chemotaxis system with signaling loop, Boundedness of classical solutions to a degenerate Keller-Segel type model with signal-dependent motilities, Dampening effects on global boundedness and asymptotic behavior in an oncolytic virotherapy model, Global boundedness for a chemotaxis-competition system with signal dependent sensitivity and loop, Asymptotic behavior of solutions to a tumor angiogenesis model with chemotaxis–haptotaxis, Boundedness and stabilization in a two-species chemotaxis-competition system with indirect signal production, Effects of signal-dependent motilities in a Keller–Segel-type reaction–diffusion system, Global boundedness for a \(N\)-dimensional two species cancer invasion haptotaxis model with tissue remodeling, Mathematical analysis of a tumor invasion model -- global existence and stability, Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network, Global well-posedness in a chemotaxis system with oxygen consumption, A new result for 2D boundedness of solutions to a chemotaxis–haptotaxis model with/without sub-logistic source, A simultaneous blow-up problem arising in tumor modeling, Global classical solutions to a higher-dimensional doubly haptotactic cross-diffusion system modeling oncolytic virotherapy, Large-data solutions in a three-dimensional chemotaxis-haptotaxis system with remodeling of non-diffusible attractant: the role of sub-linear production of diffusible signal, Dampening effects on global boundedness in a quartic haptotactic model with fusogenic oncolytic virus and syncytia, Asymptotic stability of spatial homogeneity in a haptotaxis model for oncolytic virotherapy, Blow-up vs boundedness in a two-species attraction–repulsion chemotaxis system with two chemicals, A New Result for Global Solvability of a Two Species Cancer Invasion Haptotaxis Model with Tissue Remodeling, Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues, Boundedness in a quasilinear chemotaxis-haptotaxis model of parabolic-parabolic-ODE type, Combined effects of nonlinear proliferation and logistic damping in a three-component chemotaxis system for alopecia areata, Boundedness in a two-species chemotaxis parabolic system with two chemicals

Cites Work

Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Publication:2451888&oldid=15129906"