Compact block boundary value methods for semi‐linear delay‐reaction–diffusion equations with algebraic constraints

2020 ◽  
Vol 36 (6) ◽  
pp. 1304-1317 ◽  
Author(s):  
Xiaoqiang Yan ◽  
Chengjian Zhang
Keyword(s):  
Boundary Value ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Boundary Value Methods ◽  
Block Boundary ◽  
Linear Delay ◽  
Algebraic Constraints

scholarly journals NONLINEAR WAVE EQUATIONS AND REACTION–DIFFUSION EQUATIONS WITH SEVERAL NONLINEAR SOURCE TERMS OF DIFFERENT SIGNS AT HIGH ENERGY LEVEL

2013 ◽  
Vol 54 (3) ◽  
pp. 153-170 ◽  
Author(s):  
RUNZHANG XU ◽  
YANBING YANG ◽  
SHAOHUA CHEN ◽  
JIA SU ◽  
JIHONG SHEN ◽  
...  
Keyword(s):  
Boundary Value Problem ◽  
Wave Equations ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Nonlinear Wave Equations ◽  
Initial Boundary Value

AbstractThis paper is concerned with the initial boundary value problem of a class of nonlinear wave equations and reaction–diffusion equations with several nonlinear source terms of different signs. For the initial boundary value problem of the nonlinear wave equations, we derive a blow up result for certain initial data with arbitrary positive initial energy. For the initial boundary value problem of the nonlinear reaction–diffusion equations, we discuss some probabilities of the existence and nonexistence of global solutions and give some sufficient conditions for the global and nonglobal existence of solutions at high initial energy level by employing the comparison principle and variational methods.

BIFURCATIONS OF ONE-DIMENSIONAL REACTION–DIFFUSION EQUATIONS

2001 ◽  
Vol 11 (05) ◽  
pp. 1295-1306 ◽  
Author(s):  
CHANGPIN LI ◽  
GUANRONG CHEN
Keyword(s):  
Boundary Value ◽  
Reaction Diffusion ◽  
Singularity Theory ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
One Dimensional ◽  
Boundary Value Condition

Bifurcations of a class of one-dimensional reaction–diffusion equations of the form u″+μu-uk=0, where μ is a parameter, 2≤k∈Z+, with boundary value condition u(0)=u(π)=0, are investigated. Using the singularity theory based on the Liapunov–Schmidt reduction, some characterization results are obtained.

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