Abstract
In this paper, we investigate the effect of weight function in the nonlinear part on global solvability of the Cauchy problem for a class of semi-linear hyperbolic equations with damping.
Highlights
In the case when a .x is independent of x, the existence and nonexistence of the global solutions was investigated in the papers [1,2,3,4,5,6,7,8]
We investigate the effect of weight function in the nonlinear part on global solvability of the Cauchy problem for a class of semi-linear hyperbolic equations with damping
The authors interests are focused on so called critical exponent pc n, which is the number defined by the following property: if p pc n all small data solutions of corresponding Cauchy problem have a global solution, while 1 p pc n all solutions with data positive on blow up in finite time regardless of the smallness of the data
Summary
In the case when a .x is independent of x , the existence and nonexistence of the global solutions was investigated in the papers [1,2,3,4,5,6,7,8]. The authors interests are focused on so called critical exponent pc n , which is the number defined by the following property: if p pc n all small data solutions of corresponding Cauchy problem have a global solution, while 1 p pc n all solutions with data positive on blow up in finite time regardless of the smallness of the data. In the present paper we investigate the effect of the weight function a x on global solvability of Cauchy problems (1) and (2)
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