| Abstract: |
| In this talk we first prove a quasiconvergence result (that is, the $\omega$-limit set of a solution
consists entirely of steady states) for bounded solutions of general quasilinear parabolic equations in unbounded or variable domains in one dimensional space. Then, we use this result to study a one dimensional heterogeneous reaction diffusion equation with combustion type of nonlinearity. We prove a trichotomy result on the asymptotic behavior of solutions of the Cauchy problem: any nonnegative solution converges as $t\to\infty$ to either a positive steady state, or the ignition point, or the trivial solution 0. |
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