Global existence versus finite-time blowup dichotomy for a general class of nonlinear fourth-order reaction-diffusion equations in higher dimensions

For a general domain Ω ⊂ Rᵈ Ω ⊂ R d in higher dimensions d≥ 5 d ≥ 5 , we examine the initial value problem for a class of nonlinear fourth-order reaction–diffusion equations with variable coefficients. We prove the local-in-time well-posedness (local existence, regularity estimate, continuous dependence on initial data and continuation) of the solutions in the time-weighted Sobolev space. Moreover, we investigate the global-in-time theory of the solutions (global existence or finite-time blow-up) in the Sobolev space.