Incomplete Self-Similar Blow-Up in a Semilinear Fourth-Order Reaction-Diffusion Equation

摘要

For applications of such higher-diffusion models, see surveys and references in [1, 4]. In general, higher-order semilinear parabolic equations arise in many physical applications such as thin film, convection-explosion, and lubrication theory, flame and wave propagation (the Kuramoto–Sivashinsky equation and the extended Fisher–Kolmogorov equation), phase transition at critical Lifshitz points, bi-stable systems and applications to structural mechanics. The effect of fourth-order terms on self-focusing problems in nonlinear optics are also well known in applied and mathematical literature. For a systematic treatment of extended KPPF-equations; see in Peletier-Troy