Research Announcement: Finite-time Blow Up and Long-wave Unstable Thin Film Equations

2010/08/02 by Marina Chugunova, Chugunova, Marina, Pugh, M. C. +1
Engineering · Mathematics · #35B05 #35B45 #35D05 #35D10 #35G25 #35K35 #35K65 #35Q35 #76A20 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Thin Films #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1008.0385

openalex publication_date 2010/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study short--time existence, long--time existence, finite speed of propagation, and finite--time blow--up of nonnegative solutions for long-wave unstable thin film equations h_t = -a₀(hⁿ h_xxx)_x - a₁(h^m h_x)_x with n>0, a₀ > 0, and a₁ >0. The existence and finite speed of propagation results extend those of [Comm Pure Appl Math 51:625--661, 1998]. For 0

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