Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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THE CONE PROPERTY FOR A CLASS OF PARABOLIC EQUATIONS

  • Received : 2017.03.29
  • Accepted : 2017.05.29
  • Published : 2017.06.25
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Abstract

In this note, we show that the cone property is satisfied for a class of dissipative equations of the form $u_t={\Delta}u+f(x,u,{\nabla}u)$ in a domain ${\Omega}{\subset}{\mathbb{R}}^2$ under the so called exactness condition for the nonlinear term. From this, we see that the global attractor is represented as a Lipshitz graph over a finite dimensional eigenspace.

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References

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  1. REMARKS ON THE EXISTENCE OF AN INERTIAL MANIFOLD vol.58, pp.5, 2021, https://doi.org/10.4134/jkms.j200565