Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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FINITE TIME BLOW UP OF SOLUTIONS FOR A STRONGLY DAMPED NONLINEAR KLEIN-GORDON EQUATION WITH VARIABLE EXPONENTS

  • Received : 2018.07.09
  • Accepted : 2018.11.06
  • Published : 2018.12.25
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Abstract

This paper, we investigate a strongly damped nonlinear Klein-Gordon equation with nonlinearities of variable exponent type $$u_{tt}-{\Delta}u-{\Delta}u_t+m^2u+{\mid}u_t{\mid}^{p(x)-2}u_t={\mid}u{\mid}^{q(x)-2}u$$ associated with initial and Dirichlet boundary conditions in a bounded domain. We obtain a nonexistence of solutions if variable exponents p (.), q (.) and initial data satisfy some conditions.

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References

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