Molecular Motion through a Fluctuating Bottleneck

1994 ◽  
Vol 366 ◽  
Author(s):  
N. Eizenberg ◽  
J. Klafter
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Molecular Motion ◽  
Reaction Diffusion ◽  
Time Dependent ◽  
Reaction Diffusion Equation ◽  
Langevin Equations ◽  
Molecular Pathways

ABSTRACTMolecular motion in a series of cavities dominated by time dependent bottlenecks is studied as a model for molecular pathways in biomolecules. The problem is formulated by coupled rate and Langevin equations and is shown to be equivalent to n-dimensional reaction-diffusion equation where n is the number of cavities visited by the molecules. Results are presented for two cavities and a comparison is made between steady state and non steady state results.

scholarly journals Gradient Optimal Control of the Bilinear Reaction–Diffusion Equation

2021 ◽  
Author(s):  
El Hassan Zerrik ◽  
Abderrahman Ait Aadi
Keyword(s):  
Optimal Control ◽  
Diffusion Equation ◽  
Minimization Problem ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Time Dependent ◽  
Reaction Diffusion Equation ◽  
Energy Term ◽  
Bounded Controls ◽  
Special Cases

In this chapter, we study a problem of gradient optimal control for a bilinear reaction–diffusion equation evolving in a spatial domain Ω⊂Rn using distributed and bounded controls. Then, we minimize a functional constituted of the deviation between the desired gradient and the reached one and the energy term. We prove the existence of an optimal control solution of the minimization problem. Then this control is characterized as solution to an optimality system. Moreover, we discuss two special cases of controls: the ones are time dependent, and the others are space dependent. A numerical approach is given and successfully illustrated by simulations.

New exact solutions of the reaction–diffusion equation with variable coefficients via the mathematical computation

2018 ◽  
Vol 11 (04) ◽  
pp. 1850051 ◽  
Author(s):  
Jin Hyuk Choi ◽  
Hyunsoo Kim
Keyword(s):  
Diffusion Equation ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Variable Coefficients ◽  
Time Dependent ◽  
Reaction Diffusion Equation ◽  
Painlevé Test ◽  
New Exact Solutions ◽  
Mathematical Computation

In this paper, we construct new exact solutions of the reaction–diffusion equation with time dependent variable coefficients by employing the mathematical computation via the Painlevé test. We describe the behaviors and their interactions of the obtained solutions under certain constraints and various variable coefficients.

scholarly journals Solution of nonlinear equations and computation of multiple solutions of a simple reaction-diffusion equation

2000 ◽  
Vol 42 (1) ◽  
pp. 55-64
Author(s):  
Adrian Swift ◽  
Easwaran Balakrishnan
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Nonlinear Equations ◽  
Multiple Solutions ◽  
Path Following ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Research Involvement ◽  
Path Following Methods ◽  
Nonlinear Equation Systems

AbstractThe first part of this paper starts with a brief discussion of some methods for solution of nonlinear equations which have interested the first author over the last twenty years or so. In the second part we discuss a recent research involvement, the success of which relies heavily on the numerical solution of nonlinear equation systems. We briefly describe path-following methods and then present an application to a simple steady-state reaction-diffusion equation arising in combustion theory. Results for some regular geometric shapes are shown and compared with those from an approximate method.

scholarly journals Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable

1992 ◽  
Vol 52 (3) ◽  
pp. 343-355 ◽  
Author(s):  
Shin-Hwa Wang ◽  
Nicholas D. Kazarinoff
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Space Variable ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Order Interval ◽  
Exact Number ◽  
Time Map ◽  
Steady State Solutions

AbstractWe study the bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable by modifying a “time map” technique introduced by J. Smoller and A. Wasserman. We count the exact number of steady-state solutions which are totally ordered in an order interval. We are then able to find their Conley indices and thus determine their stabilities.

scholarly journals Regularity of random attractors for stochastic reaction-diffusion equations on unbounded domains

2015 ◽  
Vol 16 (01) ◽  
pp. 1650006 ◽  
Author(s):  
Bao Quoc Tang
Keyword(s):  
Diffusion Equation ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Random Attractors ◽  
External Forces ◽  
Stochastic Reaction

The existence of a unique random attractors in [Formula: see text] for a stochastic reaction-diffusion equation with time-dependent external forces is proved. Due to the presence of both random and non-autonomous deterministic terms, we use a new theory of random attractors which is introduced in [B. Wang, J. Differential Equations 253 (2012) 1544–1583] instead of the usual one. The asymptotic compactness of solutions in [Formula: see text] is established by combining “tail estimate” technique and some new estimates on solutions. This work improves some recent results about the regularity of random attractors for stochastic reaction-diffusion equations.

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