摘要:

AbstractThis paper is concerned with some qualitative analysis for a coupled system of five reaction–diffusion equations which arises from a physiology model. The uniform boundedness of the time‐dependent solution is obtained under various boundary conditions. Sufficient conditions are also given to ensure the asymptotic stability of the non‐negative steady‐state solutions under Dirichlet or Robin boundary condition for each component. Under homogeneous Neumann boundary condition for some components the time‐dependent solution is proven to converge to a constant steady state determined by the initial

ISSN:0170-4214    

DOI:10.1002/mma.1670170302

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis article deals with flow phenomena in liquid crystal materials. The model that I analyse is that due to Ericksen for liquid crystals with variable degree of orientation. One of the goals is understanding the role of the order parameter in the model. I examine the multiplicity of solutions,phases, that occur in shear flow regimes and analyse their stability under physically realistic conditions. In particular, I show that ellipticity of the linearized system of governing equations is a consequence of the Clausius–Duhem inequalit

ISSN:0170-4214    

DOI:10.1002/mma.1670170303

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractPerturbation of a single‐degree‐of‐freedom conservative oscillator leads to the emergence and vanishing of periodic solutions and to various types of self‐excited oscillations. Using techniques from dynamical systems theory, in particular a certain Poincaré map, we establish the presence of Hopf bifurcations, various types of homoclinic bifurcations and saddle‐node bifurcations of the associated Poincaré map. The corresponding bifurcation sets in parameter space are computed explicitly by perturbation methods. The theory is applied to the generalized van der Pol and the generalized Rayleigh oscillator, and to the case of a non‐linear spring attached to a

ISSN:0170-4214    

DOI:10.1002/mma.1670170304

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe averaging method is used to approximate solutions of systems of linearly coupled, (quadratic) non‐linear dispersive wave equations, which describe extensional–torsional dynamics of a rod. Existence and uniqueness results are established. Error estimates confirm the asymptotic validity of the approximation method on a long time‐scale. The linear couplings between the equations imply that resonance can occur inside a single mode of the solution, but energy can also be transferred to other

ISSN:0170-4214    

DOI:10.1002/mma.1670170305

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670170301

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY