On the solvability of a boundary value problem for nonlinear wave equations in angular domains

2016 ◽  
Vol 52 (5) ◽  
pp. 644-666 ◽  
Author(s):  
S. S. Kharibegashvili ◽  
O. M. Jokhadze
Keyword(s):  
Boundary Value Problem ◽  
Nonlinear Wave ◽  
Wave Equations ◽  
Boundary Value ◽  
Nonlinear Wave Equations ◽  
Angular Domains

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.

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