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Global existence for Laplace reaction-diffusion equations

  • * Corresponding author: Atsushi Yagi

    * Corresponding author: Atsushi Yagi
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  • We study the initial-boundary value problem for a Laplace reaction-diffusion equation. After constructing local solutions by using the theory of abstract degenerate evolution equations of parabolic type, we show global existence under suitable assumptions on the reaction function. We also show that the problem generates a dynamical system in a suitably set universal space and that this dynamical system possesses a Lyapunov function.

    Mathematics Subject Classification: Primary: 37L05; Secondary: 35K57, 35J15.

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