Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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NONLINEAR HEAT EQUATIONS WITH TRANSCENDENTAL NONLINEARITY IN BESOV SPACES

  • Pak, Hee Chul (Department of Applied Mathematics and Institute of Basic Sciences Dankook University) ;
  • Chang, Sang-Hoon (Department of Applied Mathematics Dankook University)
  • Received : 2010.09.05
  • Accepted : 2010.11.09
  • Published : 2010.12.30
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Abstract

The existence of solutions in Besov spaces for nonlinear heat equations having transcendental nonlinearity: $$\frac{\partial}{{\partial}t}u-{\Delta}u=F(u)$$ is investigated. In particular, it is proved the local existence and blow-up phenomena of the solutions in Besov spaces for nonlinear heat equations corresponding to two transcendental nonlinear functions $F(u){\equiv}{\mid}u{\mid}e^{u^2}$ and $F(u){\equiv}e^u$ of rapid growth.

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References

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