Large-time stability of travelling waves for a class of fully nonlinear parabolic equations
Authors:
Fabio Camilli and Manuela Molinari
Journal:
Quart. Appl. Math. 60 (2002), 533-546
MSC:
Primary 35K55; Secondary 35B35
DOI:
https://doi.org/10.1090/qam/1914440
MathSciNet review:
MR1914440
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Abstract: In this paper we prove existence and ${L^{1}}$ stability of travelling waves for a class of second-order nonlinear parabolic equations in divergence form. As a consequence of the previous result, we get stability in the ${L^{\infty }}$ norm of travelling waves for a class of fully nonlinear second-order equations.
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P. Marcati, Weak Solutions to a Nonlinear Partial Differential Equation of Mixed Type, Differential Integral Equations 9, 827–848 (1996)
A. Matsumura and K. Nishihara, Asymptotic stability of traveling waves for scalar viscous conservation laws with non-convex nonlinearity, Comm. Math. Phys. 165, 83–96 (1994)
C. Mascia and R. Natalini, $L^{1}$ Nonlinear stability of travelling waves for a hyperbolic system with relaxation, J. Differential Equations 13, 321–344 (1996)
S. Osher and J. Ralston, $L^{1}$ Stability of travelling waves with applications to convective porous media flow, Comm. Pure Appl. Math. 35, 737–751 (1982)
D. Serre, $L^{1}$ -Decay and Stability of Shock Profiles, Partial Differential Equations (Praha, 1998), pp. 312–321. Research Notes in Math., vol. 406, Chapman and Hall, Boca Raton, FL., 2000
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L. Wang, On the regularity theory of fully nonlinear parabolic equations, Comm. Pure Appl. Math. 45, 255–262 (1992)
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© Copyright 2002
American Mathematical Society
