Infinite-dimensional exponential attractors for fourth-order nonlinear parabolic equations in unbounded domains

2011 ◽  
Vol 34 (8) ◽  
pp. 939-949 ◽  
Author(s):  
Messoud Efendiev
Keyword(s):  
Fourth Order ◽  
Parabolic Equations ◽  
Unbounded Domains ◽  
Nonlinear Parabolic Equations ◽  
Exponential Attractors ◽  
Infinite Dimensional ◽  
Nonlinear Parabolic

scholarly journals A class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yang Liu ◽  
Wenke Li
Keyword(s):  
Thin Films ◽  
Epitaxial Growth ◽  
Fourth Order ◽  
Parabolic Equations ◽  
Blow Up ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Nonlinear Parabolic Equations ◽  
Potential Wells ◽  
Nonlinear Parabolic

<p style='text-indent:20px;'>In this paper, the initial-boundary value problem for a class of fourth-order nonlinear parabolic equations modeling the epitaxial growth of thin films is studied. By means of the theory of potential wells, the global existence, asymptotic behavior and finite time blow-up of weak solutions are obtained.</p>

BIFURCATIONAL FEATURES IN SYSTEMS OF NONLINEAR PARABOLIC EQUATIONS WITH WEAK DIFFUSION

2005 ◽  
Vol 15 (11) ◽  
pp. 3595-3606 ◽  
Author(s):  
S. A. KASCHENKO
Keyword(s):  
Parabolic Equations ◽  
Diffusion Coefficients ◽  
Nonlinear Parabolic Equations ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
Infinite Dimensional ◽  
Spatial Systems ◽  
Nonlinear Parabolic ◽  
Parabolic Boundary Value Problems ◽  
Weak Diffusion

Asymptotic solutions of parabolic boundary value problems are studied in a neighborhood of both an equilibrium state and a cycle in near-critical cases which can be considered as infinite-dimensional due to small values of the diffusion coefficients. Algorithms are developed to construct normalized equations in such situations. Principle difference between bifurcations in two-dimensional and one-dimensional spatial systems is demonstrated.

Kinetics of oxidation of ammonia on cobalt catalyst I model of the reactor with catalytically active wall

1982 ◽  
Vol 47 (8) ◽  
pp. 2087-2096 ◽  
Author(s):  
Bohumil Bernauer ◽  
Antonín Šimeček ◽  
Jan Vosolsobě
Keyword(s):  
Parabolic Equations ◽  
Cobalt Catalyst ◽  
Nonlinear Parabolic Equations ◽  
Catalytic Reactions ◽  
Temperature Profiles ◽  
Dimensional Model ◽  
Kinetics Of Oxidation ◽  
Nonlinear Parabolic ◽  
Catalytically Active ◽  
Kinetics Of

A two dimensional model of a tabular reactor with the catalytically active wall has been proposed in which several exothermic catalytic reactions take place. The derived dimensionless equations enable evaluation of concentration and temperature profiles on the surface of the active component. The resulting nonlinear parabolic equations have been solved by the method of orthogonal collocations.

Sign in / Sign up

Export Citation Format

Share Document