Gradient-like parabolic semiflows on BUC(ℝN)

1998 ◽  
Vol 128 (6) ◽  
pp. 1281-1291 ◽  
Author(s):  
Daniel Daners ◽  
Sandro Merino
Keyword(s):  
Banach Space ◽  
Exponential Decay ◽  
Decay Estimate ◽  
Reaction Diffusion ◽  
Continuous Functions ◽  
Stationary Solutions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Uniformly Continuous

We prove that a class of weighted semilinear reaction diffusion equations on RN generates gradient-like semiflows on the Banach space of bounded uniformly continuous functions on RN. If N = 1 we show convergence to a single equilibrium. The key for getting the result is to show the exponential decay of the stationary solutions, which is obtained by means of a decay estimate of the kernel of the underlying semigroup.

scholarly journals Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift

2015 ◽  
Vol 18 (02) ◽  
pp. 1550013 ◽  
Author(s):  
Andrei Khrennikov ◽  
Sergei Kozyrev ◽  
Alf Månsson
Keyword(s):  
Dynamic Models ◽  
Molecular Motor ◽  
Reaction Diffusion ◽  
Molecular Machines ◽  
Stationary Solutions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
System Of Equations ◽  
Wavelet Theory ◽  
And Behavior

We discuss the approach to investigate molecular machines using systems of integro–differential ultrametric (p-adic) reaction–diffusion equations with drift. This approach combines the features of continuous and discrete dynamic models. We apply this model to investigation of actomyosin molecular motor. The introduced system of equations is solved analytically using p-adic wavelet theory. We find explicit stationary solutions and behavior in the relaxation regime.

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