scholarly journals Analysis of the Boundary Value and Control Problems for Nonlinear Reaction–Diffusion–Convection Equation

2001 ◽  
Vol 14 (4) ◽  
pp. 452-462
Author(s):  
Gennady V. Alekseev ◽  
Keyword(s):  
Boundary Value Problem ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Control Problems ◽  
Stability Estimates ◽  
Convection Equation ◽  
Reaction Coefficient ◽  
Diffusion Convection ◽  
And Control

The global solvability of the inhomogeneous mixed boundary value problem and control problems for the reaction–diffusion–convection equation are proved in the case when the reaction coefficient nonlinearly depends on the concentration. The maximum and minimum principles are established for the solution of the boundary value problem. The optimality systems are derived and the local stability estimates of optimal solutions are established for control problems with specific reaction coefficients

DIFFUSIVE EFFECTS ON A CATALYTIC SURFACE REACTION: AN INITIAL BOUNDARY VALUE PROBLEM IN REACTION-DIFFUSION-CONVECTION EQUATIONS

1993 ◽  
Vol 03 (01) ◽  
pp. 79-95 ◽  
Author(s):  
WEN ZHANG
Keyword(s):  
Boundary Value Problem ◽  
Surface Reaction ◽  
Boundary Value ◽  
Reaction Diffusion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Catalytic Surface ◽  
Reaction Fronts ◽  
Initial Boundary Value ◽  
Diffusion Convection

A bimolecular catalytic surface reaction is extended to include diffusion which yields mobilized coverage on the surface. We consider the reaction occurring in a tubular reactor with a convection flow where the reactants also diffuse. An initial boundary value problem in one-dimensional reaction-diffusion-convection equations is used in describing the model. We combine singular perturbation analysis with numerical simulations in studying the solution behavior in parameter space. We track the reaction front and the cause of period-2 oscillations. Compared with the case of having no surface diffusion, we observe regular oscillations instead of irregular oscillations. Compared with the nondiffusive nonconvective model, we obtain rich spatiotemporal patterns including stationary, oscillatory reaction fronts and multiple steady states.

Boundary and Interior Control for Partial Differential Equations

1975 ◽  
Vol 27 (1) ◽  
pp. 200-217 ◽  
Author(s):  
Robert Delver
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Control Problems ◽  
Partial Differential ◽  
And Control ◽  
Class Of Functions ◽  
Admissible Functions

From the time that the basic existence and regularity problems for partial differential equations have been solved many interesting new variational and control problems could be studied. In general a differential equation or boundary value problem is used to define a class of admissible functions, and then the problem is that of finding the extrema of a given functional defined on that class of functions.

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