Long-time dynamics of a bulk-surface convective Cahn--Hilliard system: Pullback attractors and convergence to equilibrium
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918383468937216 |
|---|---|
| author | Knopf, Patrik Poiatti, Andrea Stange, Jonas Yayla, Sema |
| author_facet | Knopf, Patrik Poiatti, Andrea Stange, Jonas Yayla, Sema |
| contents | We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents the associated free energy from being a Lyapunov functional, which makes the analysis of the asymptotic behavior considerably more challenging. First, we establish an instantaneous regularization property for weak solutions. Next, interpreting the evolution as a continuous two-parameter process, we prove the existence of a minimal pullback attractor. Finally, under suitable decay assumptions on the velocity fields, we show that every solution converges as $t\to\infty$ to a single steady state. The proof of this convergence relies on the Łojasiewicz--Simon inequality combined with customized decay estimates that compensate for the lack of a monotone energy functional. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_10923 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Long-time dynamics of a bulk-surface convective Cahn--Hilliard system: Pullback attractors and convergence to equilibrium Knopf, Patrik Poiatti, Andrea Stange, Jonas Yayla, Sema Analysis of PDEs 35K35, 35B40, 35Q92, 35B65 We study the long-time dynamics of a bulk-surface convective Cahn--Hilliard system describing phase separation processes with bulk-surface interaction. The presence of convection terms leads to a non-autonomous dynamical system and prevents the associated free energy from being a Lyapunov functional, which makes the analysis of the asymptotic behavior considerably more challenging. First, we establish an instantaneous regularization property for weak solutions. Next, interpreting the evolution as a continuous two-parameter process, we prove the existence of a minimal pullback attractor. Finally, under suitable decay assumptions on the velocity fields, we show that every solution converges as $t\to\infty$ to a single steady state. The proof of this convergence relies on the Łojasiewicz--Simon inequality combined with customized decay estimates that compensate for the lack of a monotone energy functional. |
| title | Long-time dynamics of a bulk-surface convective Cahn--Hilliard system: Pullback attractors and convergence to equilibrium |
| topic | Analysis of PDEs 35K35, 35B40, 35Q92, 35B65 |
| url | https://arxiv.org/abs/2603.10923 |