Well-posedness for some third-order evolution differential equations: A semigroup approach

2021/06/07 by Flank D. M. Bezerra, Bezerra, Flank D. M., Alexandre N. Carvalho +3
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Nonlinear Differential Equations Analysis #math.AP #math.FA #msc:34A08 #msc:35K10 #msc:47D03 #msc:47D06

paper · pdf · doi:10.48550/arxiv.2106.03564

26 pages, 9 figures

arxiv created 2021/06/07 · arxiv updated 2021/06/08

Abstract

In this paper, we discuss the well-posedness of the Cauchy problem associated with the third-order evolution equation in time u_ttt +A u + ηA^\frac13 u_tt +ηA^\frac23 u_t=f(u) where η>0, X is a separable Hilbert space, A:D(A)⊂ X→ X is an unbounded sectorial operator with compact resolvent, and for some λ₀>0 we have Reσ(A)>λ₀ and f:D(A^\frac13)⊂ X→ X is a nonlinear function with suitable conditions of growth and regularity.

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