Nonlinear stability of a diffusion equation
Authors:
Giovanni P. Galdi and Isom H. Herron
Journal:
Quart. Appl. Math. 42 (1984), 159-164
MSC:
Primary 35Q20; Secondary 35B35
DOI:
https://doi.org/10.1090/qam/745096
MathSciNet review:
745096
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Additional Information
G. P. Galdi and B. Straughan, Exchange of stability, symmetry and nonlinear stability, Arch. Rat. Mech. Anal, (to appear).
- Isom H. Herron, A diffusion equation illustrating spectral theory for boundary layer stability, Stud. Appl. Math. 67 (1982), no. 3, 231–241. MR 679300, DOI https://doi.org/10.1002/sapm1982673231
- O. A. Ladyženskaja, Matematicheskie voprosy dinamiki vyazkoĭ neszhimaemoĭ zhidkosti, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). MR 0155092
- L. A. Peletier, Asymptotic stability of travelling waves, Instability of continuous systems (IUTAM Sympos., Herrenalb, 1969), Springer, Berlin, 1971, pp. 418–422. MR 0367423
- D. H. Sattinger, Weighted norms for the stability of traveling waves, J. Differential Equations 25 (1977), no. 1, 130–144. MR 447813, DOI https://doi.org/10.1016/0022-0396%2877%2990185-1
- E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, at the Clarendon Press, 1946 (German). MR 0019765
G. P. Galdi and B. Straughan, Exchange of stability, symmetry and nonlinear stability, Arch. Rat. Mech. Anal, (to appear).
I. H. Herron, A diffusion equation illustrating spectral theory for boundary layer stability, Studies in Appl. Math. 67, 231–241 (1982)
O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1963
L. A. Peletier, Asymptotic stability of travelling waves, in Instability of Continuous Systems (H. Leipholz, ed.), Springer-Verlag, Berlin, 1970, 418–422
D. H. Sattinger, Weighted norms for the stability of travelling waves, J. Diff. Eqns. 25, 130–144 (1977)
E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations, University Press, Oxford, 1946
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Article copyright:
© Copyright 1984
American Mathematical Society