紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2025, 62(3), p. 411-432

MAXIMAL STRICT SOLUTIONS FOR SOME QUASILINEAR PARABOLIC SYSTEM OF HONEYCOMB CONSTRUCTION MODEL

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

text

2025-07

This paper treats the initial-boundary value problem for a quasilinear parabolic system in a two-dimensional region presented by Belić, Škarka, Deneubourg and Lax in order to describe the construction process of parallel honeycombs in a beehive. After constructing the local strict solutions by using the theory of abstract parabolic equations, we will define the maximal strict solutions. Unfortunately, we cannot give any general sufficient conditions on the parameters or initial functions for global existence, but we can investigate asymptotic behaviors of the maximal solutions as t → Tₘₐₓ. From numerical computations, we already have a number of examples which suggest the blowup of maximal solutions (i.e., Tₘₐₓ < ∞); at the end of the paper, we shall present one such numerical example.

10.18910/102432

102432

MAXIMAL STRICT SOLUTIONS FOR SOME QUASILINEAR PARABOLIC SYSTEM OF HONEYCOMB CONSTRUCTION MODEL

Departments of Mathematics, The University of Osaka and Osaka Metropolitan University

英語

2025-07

Osaka Journal of Mathematics

62

3

411

432

https://hdl.handle.net/11094/102432

10.18910/102432

https://doi.org/10.18910/102432