Construction of type I blowup solutions for a higher order semilinear parabolic equation

@article{Ghoul2018ConstructionOT,
  title={Construction of type I blowup solutions for a higher order semilinear parabolic equation},
  author={Tej-eddine Ghoul and Van Tien Nguyen and H. Van der Zaag},
  journal={Advances in Nonlinear Analysis},
  year={2018},
  volume={9},
  pages={388 - 412}
}
  • Tej-eddine Ghoul, Van Tien Nguyen, H. Van der Zaag
  • Published 2018
  • Mathematics, Physics
  • Advances in Nonlinear Analysis
  • Abstract We consider the higher-order semilinear parabolic equation ∂tu=−(−Δ)mu+u|u|p−1, $$\begin{array}{} \displaystyle \partial_t u = -(-{\it\Delta})^{m} u + u|u|^{p-1}, \end{array}$$ in the whole space ℝN, where p > 1 and m ≥ 1 is an odd integer. We exhibit type I non self-similar blowup solutions for this equation and obtain a sharp description of its asymptotic behavior. The method of construction relies on the spectral analysis of a non self-adjoint linearized operator in an appropriate… CONTINUE READING

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