Existence of global solutions for systems of reaction-diffusion equations on unbounded domains.
Badraoui, Salah (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Badraoui, Salah (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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J. I. Díaz (2001)
Extracta Mathematicae
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Pavol Quittner (1996)
Banach Center Publications
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Aliziane, T., Langlais, M. (2006)
Acta Mathematica Universitatis Comenianae. New Series
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M. Chipot (1992)
Banach Center Publications
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Hayashi, Nakao, Kaikina, E.I., Naumkin, P.I. (2007)
Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]
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Jan Cholewa, Tomasz Dlotko (2000)
Banach Center Publications
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An abstract parabolic equation with sectorial operator and continuous nonlinearity is studied in this paper. In particular, the asymptotic behavior of solutions is described within the framework of the theory of global attractors. Examples included in the final part of the paper illustrate the presented ideas.
Takeuchi, Shingo, Yokota, Tomomi (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Wojciech Mydlarczyk (1994)
Annales Polonici Mathematici
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For an initial value problem u'''(x) = g(u(x)), u(0) = u'(0) = u''(0) = 0, x > 0, some theorems on existence and uniqueness of solutions are established.
Jan Cholewa, Tomasz Dłotko (1996)
Banach Center Publications
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Global solutions of semilinear parabolic equations are studied in the case when some weak a priori estimate for solutions of the problem under consideration is already known. The focus is on the rapid growth of the nonlinear term for which existence of the semigroup and certain dynamic properties of the considered system can be justified. Examples including the famous Cahn-Hilliard equation are finally discussed.
Muntean, A. (2009)
Acta Mathematica Universitatis Comenianae. New Series
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