Incomplete Self-Similar Blow-Up in a Semilinear Fourth-Order Reaction-Diffusion Equation

Studies in Applied Mathematics ◽

10.1111/j.1467-9590.2009.00474.x ◽

2010 ◽

Vol 124 (4) ◽

pp. 347-381 ◽

Author(s):

V. A. Galaktionov

Keyword(s):

Diffusion Equation ◽

Fourth Order ◽

Blow Up ◽

Reaction Diffusion ◽

Order Reaction ◽

Reaction Diffusion Equation ◽

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Five types of blow-up in a semilinear fourth-order reaction–diffusion equation: an analytic–numerical approach

Nonlinearity ◽

10.1088/0951-7715/22/7/012 ◽

2009 ◽

Vol 22 (7) ◽

pp. 1695-1741 ◽

Author(s):

V A Galaktionov

Keyword(s):

Diffusion Equation ◽

Fourth Order ◽

Blow Up ◽

Reaction Diffusion ◽

Numerical Approach ◽

Order Reaction ◽

Reaction Diffusion Equation

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Mixed finite element method for the nonlinear time-fractional stochastic fourth-order reaction–diffusion equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2020.12.004 ◽

2021 ◽

Vol 84 ◽

pp. 39-55

Author(s):

Xinfei Liu ◽

Xiaoyuan Yang

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Diffusion Equation ◽

Fourth Order ◽

Mixed Finite Element ◽

Reaction Diffusion ◽

Mixed Finite Element Method ◽

Order Reaction ◽

Reaction Diffusion Equation ◽

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A high-order numerical method for solving the 2D fourth-order reaction-diffusion equation

Numerical Algorithms ◽

10.1007/s11075-018-0509-z ◽

2018 ◽

Vol 80 (3) ◽

pp. 849-877 ◽

Author(s):

Haixiang Zhang ◽

Xuehua Yang ◽

Da Xu

Keyword(s):

Diffusion Equation ◽

Numerical Method ◽

Fourth Order ◽

Reaction Diffusion ◽

Order Reaction ◽

Reaction Diffusion Equation

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NONLINEAR STABILITY OF UNIFORM STEADY STATES AND PRESERVATION OF SIGN FOR A TWO-DIMENSIONAL FOURTH-ORDER REACTION DIFFUSION EQUATION

Waves and Stability in Continuous Media ◽

10.1142/9789812773616_0007 ◽

2006 ◽

Author(s):

M.V. BARTUCCELLI

Keyword(s):

Diffusion Equation ◽

Fourth Order ◽

Nonlinear Stability ◽

Reaction Diffusion ◽

Steady States ◽

Order Reaction ◽

Reaction Diffusion Equation ◽

Two Dimensional

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A Linearized Second-Order Difference Scheme for the Nonlinear Time-Fractional Fourth-Order Reaction-Diffusion Equation

Numerical Mathematics Theory Methods and Applications ◽

10.4208/nmtma.oa-2017-0144 ◽

2019 ◽

Vol 12 (4) ◽

pp. 1168-1189 ◽

Author(s):

global sci

Keyword(s):

Diffusion Equation ◽

Difference Scheme ◽

Fourth Order ◽

Reaction Diffusion ◽

Order Reaction ◽

Second Order ◽

Reaction Diffusion Equation ◽

Order Difference

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A fourth-order compact difference method for the nonlinear time-fractional fourth-order reaction–diffusion equation

Engineering With Computers ◽

10.1007/s00366-021-01524-2 ◽

2021 ◽

Author(s):

Majid Haghi ◽

Mohammad Ilati ◽

Mehdi Dehghan

Keyword(s):

Diffusion Equation ◽

Fourth Order ◽

Difference Method ◽

Reaction Diffusion ◽

Order Reaction ◽

Reaction Diffusion Equation ◽

Compact Difference ◽

Compact Difference Method

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Blow-up estimates for a higher-order reaction–diffusion equation with a special diffusion process

Journal of Elliptic and Parabolic Equations ◽

10.1007/s41808-021-00125-w ◽

2021 ◽

Author(s):

Bui Le Trong Thanh ◽

Nguyen Ngoc Trong ◽

Tan Duc Do

Keyword(s):

Diffusion Equation ◽

Diffusion Process ◽

Blow Up ◽

Reaction Diffusion ◽

Higher Order ◽

Order Reaction ◽

Reaction Diffusion Equation

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Positivity and the attractor dimension in a fourth-order reaction-diffusion equation

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2001.0931 ◽

2002 ◽

Vol 458 (2022) ◽

pp. 1431-1446 ◽

Author(s):

M. V. Bartuccelli ◽

S. A. Gourley ◽

A. A. Ilyin

Keyword(s):

Diffusion Equation ◽

Fourth Order ◽

Reaction Diffusion ◽

Order Reaction ◽

Reaction Diffusion Equation ◽

Attractor Dimension

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Regularity of global attractor for the fourth-order reaction–diffusion equation

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2012.02.007 ◽

2012 ◽

Vol 17 (10) ◽

pp. 3824-3831 ◽

Author(s):

Hong Luo ◽

Qiang Zhang

Keyword(s):

Diffusion Equation ◽

Global Attractor ◽

Fourth Order ◽

Reaction Diffusion ◽

Order Reaction ◽

Reaction Diffusion Equation ◽

Regularity Of Global Attractor

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Instabilities and propagation properties in a fourth-order reaction–diffusion equation

Applied Mathematics and Computation ◽

10.1016/j.amc.2014.01.035 ◽

2014 ◽

Vol 231 ◽

pp. 395-406

Author(s):

Samir A. Shamseldeen

Keyword(s):

Diffusion Equation ◽

Fourth Order ◽

Reaction Diffusion ◽

Order Reaction ◽

Reaction Diffusion Equation ◽

Propagation Properties

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