Existence and asymptotic behavior of solutions of the Dirichlet problem for a nonlinear pseudoparabolic equation
| dc.contributor.author | Ngoc, Le Thi Phuong | |
| dc.contributor.author | Yen, Dao Thi Hai | |
| dc.contributor.author | Long, Nguyen Thanh | |
| dc.date.accessioned | 2021-12-17T14:50:29Z | |
| dc.date.available | 2021-12-17T14:50:29Z | |
| dc.date.issued | 2018-01-04 | |
| dc.description.abstract | This article concerns the initial-boundary value problem for non-linear pseudo-parabolic equation ut - uxxt - (1 + μ(ux))uxx + (1 + σ(ux))u = ƒ(x, t), 0 < x < 1, 0 < t < T, u(0, t) = u(1, t) = 0, u(x, 0) = ũ0(x), where ƒ, ũ0, μ, σ are given functions. Using the Faedo-Galerkin method and the compactness method, we prove that there exists a unique weak solution u such that u ∈ L∞ (0, T; H¹₀ ∩ H²), u′ ∈ L²(0, T; H¹₀) and ∥u∥L∞(QT) ≤ max{∥ũ0∥L∞(Ω), ∥ƒ∥L∞(QT}. Also we prove that the problem has a unique global solution with H1-norm decaying exponentially as t → +∞. Finally, we establish the existence and uniqueness of a weak solution of the problem associated with a periodic condition. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 20 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Ngoc, L. T. P., Yen, D. T. H., & Long, N. T. (2018). Existence and asymptotic behavior of solutions of the Dirichlet problem for a nonlinear pseudoparabolic equation. <i>Electronic Journal of Differential Equations, 2018</i>(04), pp. 1-20. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/15059 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2018, San Marcos, Texas: Texas State University and University of North Texas. | |
| dc.subject | Nonlinear pseudoparabolic equation | |
| dc.subject | Asymptotic behavior | |
| dc.subject | Exponential decay | |
| dc.subject | Periodic weak solution | |
| dc.subject | Faedo-Galerkin method | |
| dc.title | Existence and asymptotic behavior of solutions of the Dirichlet problem for a nonlinear pseudoparabolic equation | |
| dc.type | Article |