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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2019.1
- 수록면
- 1,365 - 1,388 (24page)
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In this paper we consider a class of nonlinear nonlocal parabolic equations involving $p$-Laplacian operator where the nonlocal quantity is present in the diffusion coefficient which depends on $L^p$-norm of the gradient and the nonlinear term is of polynomial type. We first prove the existence and uniqueness of weak solutions by combining the compactness method and the monotonicity method. Then we study the existence of global attractors in various spaces for the continuous semigroup generated by the problem. Finally, we investigate the existence and exponential stability of weak stationary solutions to the problem.
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참고문헌 (32)
참고문헌 신청
Azmy S. Ackleh / 2000 / Existence-uniqueness and long time behavior for a class of nonlocal nonlinear parabolic evolution equations / Proceedings of the American Mathematical Society 128(12):3483~3493
Rui M.P. Almeida / 2016 / On a nonlocal degenerate parabolic problem / Nonlinear Analysis: Real World Applications 27:146~157
C. T. Anh / 2010 / Attractors for quasilinear parabolic equations involving weighted p-Laplacian operators / Vietnam J. Math 38(3):261~280
Cung The Anh / 2009 / Long-time behavior for quasilinear parabolic equations involving weighted -Laplacian operators / Nonlinear Analysis: Theory, Methods & Applications 71(10):4415~4422
Cung The Anh / 2010 / On quasilinear parabolic equations involving weighted p-Laplacian operators / Nonlinear Differential Equations and Applications NoDEA 17(2):195~212
Rui M.P. Almeida / 2016 / On a nonlocal degenerate parabolic problem / Nonlinear Analysis: Real World Applications 27:146~157
C. T. Anh / 2010 / Attractors for quasilinear parabolic equations involving weighted p-Laplacian operators / Vietnam J. Math 38(3):261~280
Cung The Anh / 2009 / Long-time behavior for quasilinear parabolic equations involving weighted -Laplacian operators / Nonlinear Analysis: Theory, Methods & Applications 71(10):4415~4422
Cung The Anh / 2010 / On quasilinear parabolic equations involving weighted p-Laplacian operators / Nonlinear Differential Equations and Applications NoDEA 17(2):195~212
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