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Asymptotic and quenching behaviors of semilinear parabolic systems with singular nonlinearities

  • *Corresponding author

    *Corresponding author

The corresponding author is sponsored by "Chenguang Program" supported by Shanghai Educational Development Foundation and Shanghai Municipal Education Commission [grant number: 13CG20]; NSFC [grant number: 11431005]; and STCSM [grant number: 18dz2271000]

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  • In this paper, we consider a family of parabolic systems with singular nonlinearities. We study the classification of global existence and quenching of solutions according to parameters and initial data. Furthermore, the rate of the convergence of the global solutions to the minimal steady state is given. Due to the lack of variational characterization of the first eigenvalue to the linearized elliptic problem associated with our parabolic system, some new ideas and techniques are introduced.

    Mathematics Subject Classification: Primary: 35B40, 35K51, 35K58, 35A01, 35B44; Secondary: 53C35.

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  • Figure 1.  The critical curve $ \Gamma $ in $ ( \lambda,\mu) $-plane

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