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Stability of traveling waves with critical speeds for $P$-degree Fisher-type equations
This paper is concerned with the stability of the traveling front
solutions with critical speeds for a class of $p$-degree Fisher-type
equations. By detailed spectral analysis and sub-supper solution
method, we first show that the traveling front solutions with
critical speeds are globally exponentially stable in some
exponentially weighted spaces. Furthermore by Evans's function
method,
appropriate space decomposition and detailed semigroup decaying
estimates, we can prove that the waves with critical speeds are
locally asymptotically stable in some polynomially weighted spaces,
which verifies some asymptotic phenomena obtained by numerical
simulations.