Global bounds for a class of quasilinear parabolic equations.
Horn, Werner (2002)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Displaying similar documents to “A priori bounds for global solutions of a semilinear parabolic problem.”
Global bounds for a class of quasilinear parabolic equations.
Transition from decay to blow-up in a parabolic system.
Quittner, Pavol (1998)
Archivum Mathematicum
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Optimality conditions for semilinear parabolic equations with controls in leading term
Hongwei Lou (2011)
ESAIM: Control, Optimisation and Calculus of Variations
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An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of homogenizing spike variation. Results for problems with state constraints are also stated.
On the global attractors for a class of semilinear degenerate parabolic equations
Cung The Anh, Nguyen Dinh Binh, Le Thi Thuy (2010)
Annales Polonici Mathematici
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We prove the existence and upper semicontinuity with respect to the nonlinearity and the diffusion coefficient of global attractors for a class of semilinear degenerate parabolic equations in an arbitrary domain.
Global existence and long-time behavior of solutions to a class of degenerate parabolic equations
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.
A priori bounds for solutions of parabolic problems and applications
Quittner, Pavol
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A priori bounds for solutions of parabolic problems and applications
Pavol Quittner (2002)
Mathematica Bohemica
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We review some recent results concerning a priori bounds for solutions of superlinear parabolic problems and their applications.
Existence of global solution for a nonlocal parabolic problem.
El Hachimi, Abderrahmane, Sidi Ammi, Moulay Rchid (2005)
Electronic Journal of Qualitative Theory of Differential Equations [electronic only]
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A priori estimates of solutions of superlinear problems
Pavol Quittner (2001)
Mathematica Bohemica
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In this survey we consider superlinear parabolic problems which possess both blowing-up and global solutions and we study a priori estimates of global solutions.
Global Attractor for a Fourth-Order Parabolic Equation Modeling Epitaxial Thin Film Growth
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.
Global existence for semilinear parabolic systems.
Herbert Amann (1985)
Journal für die reine und angewandte Mathematik
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On the parabolic-elliptic limit of the doubly parabolic Keller-Segel system modelling chemotaxis
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.