Blow up for a nonlinear degenerate parabolic equation
Fila, M., Filo, J.
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Fila, M., Filo, J.
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Marras, M. (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 35K55, 35K60. We investigate the blow-up of the solutions to a nonlinear parabolic system with Robin boundary conditions and time dependent coefficients. We derive sufficient conditions on the nonlinearities and the initial data in order to obtain explicit lower and upper bounds for the blow up time t*.
Zhou, Jun (2007)
Surveys in Mathematics and its Applications
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Korpusov, M.O., Sveshnikov, A.G. (2005)
Sibirskij Matematicheskij Zhurnal
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Youpeng Chen, Baozhu Zheng (2015)
Annales Polonici Mathematici
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This paper deals with the blow-up properties of positive solutions to a localized singular parabolic equation with weighted nonlocal nonlinear boundary conditions. Under certain conditions, criteria of global existence and finite time blow-up are established. Furthermore, when q=1, the global blow-up behavior and the uniform blow-up profile of the blow-up solution are described; we find that the blow-up set is the whole domain [0,a], including the boundary, in contrast to the case of...
Zhou, Jun, Mu, Chunlai (2010)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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Piotr Biler, Tadeusz Nadzieja (1995)
Applicationes Mathematicae
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Radially symmetric solutions of a nonlocal Fokker-Planck equation describing the evolution of self-attracting particles in a bounded container are studied. Conditions ensuring either global-in-time existence of solutions or their finite time blow up are given.
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.
L.A. Peletier, B. Kawohl (1989)
Mathematische Zeitschrift
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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...
Liu, Changchun (2006)
Lobachevskii Journal of Mathematics
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Rossi, J.D. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Changchun Liu (2013)
Annales Polonici Mathematici
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We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.
Oleh Buhrii, Nataliya Buhrii (2017)
Open Mathematics
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Some nonlinear integro-differential equations of fourth order with variable exponents of the nonlinearity are considered. The initial-boundary value problem for these equations is investigated and the existence theorem for the problem is proved.
Andrzej Raczyński (2004)
Banach Center Publications
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We study the existence of solutions to a nonlinear parabolic equation describing the temporal evolution of a cloud of self-gravitating particles with a given external potential. The initial data are in spaces of (generalized) pseudomeasures. We prove existence of local and global-in-time solutions, and also a kind of stability of global solutions.
Carole Rosier, Lionel Rosier (2004)
Banach Center Publications
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Results on the global existence and uniqueness of variational solutions to an elliptic-parabolic problem occurring in statistical mechanics are provided.