| Abstract: |
| This talk considers the global well-posedness and the longtime dynamics for a class of strongly damped wave equations with evolutional $p(x,t)$-Laplacian, $q(x,t)$-growth source term, and the perturbed parameter $\lambda\in [0,1]$. By using the monotone operator technique and the quasi-stability method, we show the global well-posedness of weak solutions in the time-dependent phase space $[W_0^{1, p(\cdot, t)}(\Omega)\cap L^{q(\cdot, t)}(\Omega)]\times L^2(\Omega)$ and the existence of pullback $\mathscr D$-attractor and pullback $\mathscr D$-exponential attractor, which are also continuous concerning the parameter $\lambda$. This work also establishes the additional regularity of weak solutions and attractors in the semilinear case, which extends the analysis and the results for these types of models with constant exponent nonlinearities. |
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