Abstract
In this paper, the existence and blow-up property of solutions to an initial and boundary value problem for a nonlinear parabolic system with variable exponents is studied. Meanwhile, the blow-up property of solutions for a nonlinear hyperbolic system is also obtained.
Highlights
There have been many results about the existence, boundedness and blow-up properties of the solutions; we refer the readers to the bibliography given in [ – ]
The aim of this paper is to extend the results in [, ] to the case of parabolic system ( . ) and hyperbolic system ( . )
As far as we know, this seems to be the first paper, where the blow-up phenomenon is studied with variable exponents for the initial and boundary value problem to some parabolic and hyperbolic systems
Summary
There have been many results about the existence, boundedness and blow-up properties of the solutions; we refer the readers to the bibliography given in [ – ]. The authors investigated the boundedness and blow-up of solutions to problem The author studied the blowup property of solutions for parabolic and hyperbolic problems.
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