Titlebook: Studies in Non-Linear Stability Theory; Wiktor Eckhaus Book 1965 Springer-Verlag, Berlin · Heidelberg 1965 Systemtheorie.differential equa

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Analysis of Some One-Dimensional Problems,r the non-linear stability problems we have made various assumptions, concerning the outcome of the linearized theory, the behaviour of coefficients, etc. We shall presently illustrate these developments by some specific examples, which show that the hypothesis which have been made are realistic, th

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A Class of Problems in Two-Dimensional Space,omplexity than the one-dimensional stability problems studied in the preceding chapters. We shall find however, at various points of our study, that many concepts introduced in the investigation of the one-dimensional problems still retain their utility. Indeed, from the point of view of mathematica

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0081-3877 and it will probably take some time before our understanding of those problems reaches some degree of maturity. The passage from the more classical linear analysis to a non-linear analysis increases the mathematical complexity of the stability theory to a point where it may become discouraging, whi

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Stability of Periodic Solutions,n a proper formulation of the stability problem general . perturbations must be studied. Thus we should consider initial conditions such that . ≠ 0 for all values of .. The analysis of the preceding chapter is then simply not applicable.

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A Class of Problems in One-Dimensional Space,nding of certain non-linear phenomena. Moreover, from the mathematical point of view, the problems to be considered already contain certain difficulties which are typical of non-linear stability theory, so that their study can be considered as a first step in the construction of adequate methods of analysis for problems of greater complexity.

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Analysis of Some One-Dimensional Problems,etc. We shall presently illustrate these developments by some specific examples, which show that the hypothesis which have been made are realistic, that is, that in certain problems of interest the assumptions are indeed verified.