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Existence and stability of travelling waves in fixed‐bed reactors
Author(s) -
Knöpp Ulrich,
Eckhaus W.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110504
Subject(s) - mathematics , mathematical analysis , stability (learning theory) , boundary value problem , phase plane , traveling wave , plane (geometry) , phase space , phase velocity , distribution (mathematics) , space (punctuation) , plane wave , phase (matter) , nonlinear system , geometry , physics , linguistics , philosophy , quantum mechanics , machine learning , computer science , optics , thermodynamics
The model equations of the catalytic fixed‐bed reactor often possess solutions in the form of travelling wave fronts similar to the well‐known case of Fisher's equation. The mathematical investigation of these waves requires searching for solutions of singular boundary value problems in the phase plane or in the three‐dimensional phase space. In this paper necesary and sufficient conditions are derived which are to be satisfied by the model parameters and the propagation velocity of the wave front if wave solutions exist. Moreover, sufficient conditions for the asymptotic stability of these solutions are proved where the perturbations are supposed to belong to a certain weighted L 2 ‐space. Finally, the connection between the initial distribution of the state variable and the velocity of the wave is discussed.