scholarly journals ON THE EXISTENCE AND NONEXISTENCE OF SOLUTIONS FOR SOME NONLINEAR WAVE EQUATIONS OF KIRCHHOFF TYPE

2010 ◽  
Vol 14 (4) ◽  
pp. 1543-1570 ◽  
Author(s):  
Shun-Tang Wu ◽  
Long-Yi Tsai
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Kirchhoff Type ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions

scholarly journals On a system of nonlinear wave equations of Kirchhoff type with a strong dissipation

2007 ◽  
Vol 38 (1) ◽  
pp. 1-20 ◽  
Author(s):  
Shun-Tang Wu ◽  
Long-Yi Tsai
Keyword(s):  
Nonlinear Wave ◽  
Wave Equations ◽  
Blow Up ◽  
Local Existence ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Wave Equations ◽  
Banach Fixed Point Theorem ◽  
Kirchhoff Type ◽  
Initial Boundary Value

The initial boundary value problem for systems of nonlinear wave equations of Kirchhoff type with strong dissipation in a bounded domain is considered. We prove the local existence of solutions by Banach fixed point theorem and blow-up of solutions by energy method. Some estimates for the life span of solutions are given.

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