Alain Miranville (2006)
Open Mathematics
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Our aim in this paper is to study the long time behavior of a class of doubly nonlinear parabolic equations. In particular, we prove the existence of the global attractor which has, in one and two space dimensions, finite fractal dimension.
Caristi, Gabriella (2001)
Abstract and Applied Analysis
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Temur Jangveladze, Zurab Kiguradze (2011)
Open Mathematics
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Large time behavior of the solution to the nonlinear integro-differential equation associated with the penetration of a magnetic field into a substance is studied. Furthermore, the rate of convergence is given. Initial-boundary value problem with mixed boundary conditions is considered.
Toyohiko Aiki, Hitoshi Imai (2000)
Czechoslovak Mathematical Journal
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Feng, Xueshang (1995)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Karachalios, Nikos, Stavrakakis, Nikos, Xanthopoulos, Pavlos (2003)
Abstract and Applied Analysis
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Brice Bangola (2013)
Open Mathematics
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We deal with a generalization of the Caginalp phase-field model associated with Neumann boundary conditions. We prove that the problem is well posed, before studying the long time behavior of solutions. We establish the existence of the global attractor, but also of exponential attractors. Finally, we study the spatial behavior of solutions in a semi-infinite cylinder, assuming that such solutions exist.
Liu, Changchun, Guan, Yujing, Wang, Zhao (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Wojciech M. Zajączkowski
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We consider the motion of a viscous compressible barotropic fluid in bounded by a free surface which is under constant exterior pressure. For a given initial density, initial domain and initial velocity we prove the existence of local-in-time highly regular solutions. Next assuming that the initial density is sufficiently close to a constant, the initial pressure is sufficiently close to the external pressure, the initial velocity is sufficiently small and the external force vanishes...
Shujun You, Boling Guo, Xiaoqi Ning (2012)
Applications of Mathematics
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This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.