Explicit exponential decay bounds in quasilinear parabolic problems.
Philippin, G.A., Vernier Piro, S. (1999)
Journal of Inequalities and Applications [electronic only]
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Philippin, G.A., Vernier Piro, S. (1999)
Journal of Inequalities and Applications [electronic only]
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François-Xavier Le Dimet, Victor Petrovich Shutyaev, Jiafeng Wang, Mu Mu (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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The soil water movement model governed by the initial-boundary value problem for a quasilinear 1-D parabolic equation with nonlinear coefficients is considered. The generalized statement of the problem is formulated. The solvability of the problem is proved in a certain class of functional spaces. The data assimilation problem for this model is analysed. The numerical results are presented.
Piotr Biler, Lorenzo Brandolese (2009)
Studia Mathematica
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We establish new results on convergence, in strong topologies, of solutions of the parabolic-parabolic Keller-Segel system in the plane to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under a natural smallness assumption.
Kaouther Ammar, Jaouad Bennouna, Hicham Redwane (2014)
Applicationes Mathematicae
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We prove the existence and uniqueness of a renormalized solution for a class of nonlinear parabolic equations with no growth assumption on the nonlinearities.
Ji Liu, Jia-Shan Zheng (2015)
Czechoslovak Mathematical Journal
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We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of...
A. Grimaldi, F. Ragnedda (1983)
Annales Polonici Mathematici
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Ning Duan, Xiaopeng Zhao (2012)
Bulletin of the Polish Academy of Sciences. Mathematics
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This paper is concerned with a fourth-order parabolic equation which models epitaxial growth of nanoscale thin films. Based on the regularity estimates for semigroups and the classical existence theorem of global attractors, we prove that the fourth order parabolic equation possesses a global attractor in a subspace of H², which attracts all the bounded sets of H² in the H²-norm.
Cung The Anh, Phan Quoc Hung (2008)
Annales Polonici Mathematici
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We study the global existence and long-time behavior of solutions for a class of semilinear degenerate parabolic equations in an arbitrary domain.
H. Ugowski (1972)
Annales Polonici Mathematici
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H. Ugowski (1973)
Annales Polonici Mathematici
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J. Murzewski, A. Sowa (1972)
Applicationes Mathematicae
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El Hachimi, Abderrahmane, Sidi Ammi, Moulay Rchid (2005)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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