| Abstract: |
| This talk is concerned with the stability of sharp traveling wave for
Burgers-Fisher-KPP equations with degenerate diffusion. We show the evolution
of free boundary of the solution to Cauchy problem and the convergence
to sharp traveling wave with almost exponential decay rates. Here,
a key difficulty lies in the intrinsic presence of nonlinear advection effect.
After providing an delicate analysis for the relations between the nonlinear
advection and the critical wave speed, we develop an equivalent transformation
of the evolution estimation of the semi-supported free boundary by
analysis the compact supported boundary behavior of the solutions. The new
method overcomes the diffculties of the non-integrability of the generalized
derivatives of sharp traveling waves near the compacted supported boundary. |
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