| Autor: |
Rong Guo, Xuan Leng |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
Boundary Value Problems, Vol 2024, Iss 1, Pp 1-19 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
1687-2770 |
| DOI: |
10.1186/s13661-024-01824-8 |
| Popis: |
Abstract This paper is concerned with the existence and uniqueness of global attractors for a class of degenerate parabolic equations with memory on R n $\mathbb{R}^{n}$ . Since the corresponding equation includes the degenerate term div { a ( x ) ∇ u } $\operatorname{div}\{a(x)\nabla u\}$ , it requires us to give appropriate assumptions about the weight function a ( x ) $a(x)$ for studying our problem. Based on this, we first obtain the existence of a bounded absorbing set, then verify the asymptotic compactness of a solution semigroup via the asymptotic contractive semigroup method. Finally, the existence and uniqueness of global attractors are proved. In particular, the nonlinearity f satisfies the polynomial growth of arbitrary order p − 1 $p-1$ ( p ≥ 2 $p\geq 2$ ) and the idea of uniform tail-estimates of solutions is employed to show the strong convergence of solutions. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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