Long-time dynamics of Kirchhoff equations with exponential nonlinearities

Our aim in this paper is to study the initial boundary problem for the two-dimensional Kirchhoff type wave equation with an exponentially growing source term. We first prove that the Kirchhoff wave model is globally well-posed in (H01(Ω)∩L∞(Ω))×L2(Ω), which covers the case of degenerate stiffness coefficient, and then obtain that the semigroup generated by the problem has a global attractor in the corresponding phase space. We also point out that the above results are still true in the natural energy space H01(Ω)×L2(Ω).Our aim in this paper is to study the initial boundary problem for the two-dimensional Kirchhoff type wave equation with an exponentially growing source term. We first prove that the Kirchhoff wave model is globally well-posed in (H01(Ω)∩L∞(Ω))×L2(Ω), which covers the case of degenerate stiffness coefficient, and then obtain that the semigroup generated by the problem has a global attractor in the corresponding phase space. We also point out that the above results are still true in the natural energy space H01(Ω)×L2(Ω).