Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion

John Barrett; Klaus Deckelnick

doi:10.4171/ifb/284

Existence and approximation of a nonlinear degenerate parabolic system modelling acid-mediated tumour invasion

Interfaces and Free Boundaries ◽

10.4171/ifb/284 ◽

2012 ◽

Vol 14 (3) ◽

pp. 343-363

Author(s):

John Barrett ◽

Klaus Deckelnick

Keyword(s):

Parabolic System ◽

System Modelling ◽

Tumour Invasion ◽

Degenerate Parabolic System ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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A nonlinear degenerate parabolic system with non-local source and crosswise-diffusion

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-003-1078-z ◽

2003 ◽

Vol 54 (3) ◽

pp. 503-516 ◽

Cited By ~ 2

Author(s):

W. Deng ◽

Y. Li ◽

C. Xie

Keyword(s):

Parabolic System ◽

Local Source ◽

Degenerate Parabolic System ◽

Non Local ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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Blow-up and life span estimates for a class of nonlinear degenerate parabolic system with time-dependent coefficients

Acta Mathematica Scientia ◽

10.1016/s0252-9602(17)30052-8 ◽

2017 ◽

Vol 37 (4) ◽

pp. 974-984 ◽

Cited By ~ 2

Author(s):

Anyin XIA ◽

Mingshu FAN ◽

Shan LI

Keyword(s):

Life Span ◽

Parabolic System ◽

Blow Up ◽

Time Dependent ◽

Degenerate Parabolic System ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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Liouville-Type Theorem for a Nonlinear Degenerate Parabolic System of Inequalities

Mathematical Notes ◽

10.1134/s0001434618010170 ◽

2018 ◽

Vol 103 (1-2) ◽

pp. 155-163 ◽

Cited By ~ 13

Author(s):

H. Wu

Keyword(s):

Parabolic System ◽

Type Theorem ◽

Degenerate Parabolic System ◽

Liouville Type ◽

Liouville Type Theorem ◽

System Of Inequalities ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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On the Large Time Behavior of Solutions of Some Nonlinear Degenerate Parabolic System

Finite or infinite dimensional complex analysis ◽

10.1201/9780429187681-40 ◽

2019 ◽

pp. 353-362

Author(s):

Tokumori Nanbu

Keyword(s):

Parabolic System ◽

Large Time ◽

Large Time Behavior ◽

Time Behavior ◽

Degenerate Parabolic System ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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On the existence of weak solutions of nonlinear degenerate parabolic system with variable exponents

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.09.019 ◽

2018 ◽

Vol 75 (1) ◽

pp. 322-334 ◽

Cited By ~ 3

Author(s):

L. Shangerganesh ◽

N. Nyamoradi ◽

V.N. Deiva Mani ◽

S. Karthikeyan

Keyword(s):

Parabolic System ◽

Weak Solutions ◽

Variable Exponents ◽

Degenerate Parabolic System ◽

Existence Of Weak Solutions ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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Global solutions and blow-up problems for a nonlinear degenerate parabolic system coupled via nonlocal sources

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.11.023 ◽

2007 ◽

Vol 333 (2) ◽

pp. 984-1007 ◽

Cited By ~ 9

Author(s):

Haihua Lu ◽

MingXin Wang

Keyword(s):

Parabolic System ◽

Blow Up ◽

Global Solutions ◽

Degenerate Parabolic System ◽

Nonlocal Sources ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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CONTROLLABILITY OF A NONLINEAR DEGENERATE PARABOLIC SYSTEM WITH BILINEAR CONTROL

Control Theory and Related Topics ◽

10.1142/9789812790552_0021 ◽

2007 ◽

Author(s):

PING LIN ◽

HANG GAO ◽

XU LIU

Keyword(s):

Parabolic System ◽

Degenerate Parabolic System ◽

Bilinear Control ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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Some results on controllability of a nonlinear degenerate parabolic system by bilinear control

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.03.079 ◽

2007 ◽

Vol 326 (2) ◽

pp. 1149-1160 ◽

Cited By ~ 10

Author(s):

Ping Lin ◽

Hang Gao ◽

Xu Liu

Keyword(s):

Parabolic System ◽

Degenerate Parabolic System ◽

Bilinear Control ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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A nonlocal and fully nonlinear degenerate parabolic system from strain-gradient plasticity

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2011.15.15 ◽

2011 ◽

Vol 15 (1) ◽

pp. 15-43

Author(s):

Michiel Bertsch ◽

◽

Roberta Dal Passo ◽

Lorenzo Giacomelli ◽

Giuseppe Tomassetti ◽

...

Keyword(s):

Parabolic System ◽

Strain Gradient ◽

Strain Gradient Plasticity ◽

Gradient Plasticity ◽

Degenerate Parabolic System ◽

Fully Nonlinear ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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Finite-element approximation of a nonlinear degenerate parabolic system describing bacterial pattern formation

Interfaces and Free Boundaries ◽

10.4171/ifb/62 ◽

2002 ◽

pp. 277-307 ◽

Cited By ~ 4

Author(s):

John Barrett ◽

Robert Nürnberg

Keyword(s):

Finite Element ◽

Pattern Formation ◽

Parabolic System ◽

Finite Element Approximation ◽

Element Approximation ◽

Degenerate Parabolic System ◽

Degenerate Parabolic ◽

Nonlinear Degenerate ◽

Nonlinear Degenerate Parabolic System

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