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In this paper we study the existence and long-time behavior of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted $p$-Laplacian operators with a new class of nonlinearities. First, we prove the existence and uniqueness of weak solutions by combining the compactness and monotone methods and the weak convergence techniques in Orlicz spaces. Then, we prove the existence of global attractors by using the asymptotic {\it a priori} estimates method.
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참고문헌 (13)
참고문헌 신청
Cung The Anh / 2010 / On the global attractors for a class of semilinear degenerate parabolic equations / Annales Polonici Mathematici 98(1):71~89
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
Paolo Caldiroli / 2000 / On a variational degenerate elliptic problem / NoDEA : Nonlinear Differential Equations and Applications 7(2):187~199
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
Paolo Caldiroli / 2000 / On a variational degenerate elliptic problem / NoDEA : Nonlinear Differential Equations and Applications 7(2):187~199
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