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Inertial manifolds of damped semilinear wave equations. (English) Zbl 0699.35179

We are concerned with the qualitative dynamics of a one-dimensional semilinear damped wave equation and its dependence with respect to the coefficient of the second-order time derivative, hereafter denoted by \(\epsilon^ 2\), this parameter being considered to vary right up to the limiting value \(\epsilon^ 2=0\), in which case the equation turns into a semilinear diffusion one. We give an account of the results obtained by the first author [Pitman Res. Notes Math. Ser. 155, 172-183 (1987; Zbl 0642.35061)] and by the two authors [NATO ASI Ser., Ser. F 37, 187-210 (1987; Zbl 0642.35062) and J. Differ. Equations 78, No.2, 262-307 (1989; Zbl 0699.35177)].

MSC:

35L70 Second-order nonlinear hyperbolic equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35K57 Reaction-diffusion equations
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References:

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