Asymptotic behavior for a class of parabolic equations in weighted variable Sobolev spaces

2018 ◽  
Vol 111 (1) ◽  
pp. 43-68
Author(s):  
Sergey Shmarev ◽  
Jacson Simsen ◽  
Mariza Stefanello Simsen ◽  
Marcos Roberto T. Primo
Keyword(s):  
Asymptotic Behavior ◽  
Sobolev Spaces ◽  
Parabolic Equations ◽  
Weighted Variable

scholarly journals Asymptotic Behavior of Solutions of Parabolic Equations with Unbounded Coefficients

1970 ◽  
Vol 37 ◽  
pp. 5-12 ◽  
Author(s):  
Tadashi Kuroda
Keyword(s):  
Asymptotic Behavior ◽  
Euclidean Space ◽  
Parabolic Equations ◽  
Half Line ◽  
Dimensional Euclidean Space ◽  
Asymptotic Behavior Of Solutions ◽  
Unbounded Coefficients ◽  
The Real

Let Rn be the n-dimensional Euclidean space, each point of which is denoted by its coordinate x = (x1,...,xn). The variable t is in the real half line [0, ∞).

The limiting Behavior of Solutions to Inhomogeneous Eigenvalue Problems in Orlicz-Sobolev Spaces

2014 ◽  
Vol 14 (4) ◽  
Author(s):  
Marian Bocea ◽  
Mihai Mihăilescu ◽  
Denisa Stancu-Dumitru
Keyword(s):  
Asymptotic Behavior ◽  
Sobolev Spaces ◽  
Eigenvalue Problems ◽  
Limiting Behavior

AbstractThe asymptotic behavior of the sequence {u

Convergence to travelling fronts in semilinear parabolic equations

1978 ◽  
Vol 80 (3-4) ◽  
pp. 213-234 ◽  
Author(s):  
Franz Rothe
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Parabolic Equations ◽  
Step Function ◽  
Wave Type ◽  
All Solutions ◽  
Asymptotic Speed ◽  
Rate Of Decay ◽  
Travelling Fronts ◽  
Semilinear Parabolic

SynopsisWe study the convergence to the stationary state for the parabolic equation u, = uxx + F(u). There exist wave-type solutions u(x, t) = φ(x − ct) for a continuum of velocities c. In the asymptotic behavior of this equation was investigated for a step function as initial data. In this paper we obtain the asymptotic behavior for a large class of monotone initial data.All solutions with initial data in this class evolve to wave-type solutions, where the rate of decay of the initial data determines the asymptotic speed.

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