Transient behavior analysis of vibrationally controlled nonlinear parabolic systems with Neumann boundary conditions

1993 ◽  
Vol 38 (10) ◽  
pp. 1603-1607 ◽  
Author(s):  
J. Bentsman ◽  
K.-S. Hong
Keyword(s):  
Boundary Conditions ◽  
Behavior Analysis ◽  
Neumann Boundary ◽  
Parabolic Systems ◽  
Transient Behavior ◽  
Neumann Boundary Conditions ◽  
Nonlinear Parabolic Systems ◽  
Nonlinear Parabolic

Stability Criterion For Linear Oscillatory Parabolic Systems

1992 ◽  
Vol 114 (1) ◽  
pp. 175-178 ◽  
Author(s):  
Keum S. Hong ◽  
Joseph Bentsman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Numerical Simulations ◽  
Stability Criterion ◽  
Neumann Boundary ◽  
Parabolic Systems ◽  
Neumann Boundary Conditions ◽  
Distributed Parameter ◽  
Parabolic Partial Differential Equations

This paper presents a stability criterion for a class of distributed parameter systems governed by linear oscillatory parabolic partial differential equations with Neumann boundary conditions. The results of numerical simulations that support the criterion are presented as well.

Blowup properties for several diffusion systems with localised sources

2006 ◽  
Vol 48 (1) ◽  
pp. 37-56 ◽  
Author(s):  
Zhaoyin Xiang ◽  
Qiong Chen ◽  
Chunlai Mu
Keyword(s):  
Cauchy Problem ◽  
Boundary Conditions ◽  
Neumann Boundary ◽  
Parabolic Systems ◽  
Neumann Boundary Conditions ◽  
Nonlocal Problems ◽  
Blowup Rate ◽  
Diffusion Systems ◽  
Blowup Criterion ◽  
The Cauchy Problem

AbstractThis paper investigates the Cauchy problem for two classes of parabolic systems with localised sources. We first give the blowup criterion, and then deal with the possibilities of simultaneous blowup or non-simultaneous blowup under some suitable assumptions. Moreover, when simultaneous blowup occurs, we also establish precise blowup rate estimates. Finally, using similar ideas and methods, we shall consider several nonlocal problems with homogeneous Neumann boundary conditions.

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