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Enhancement of the traveling front speeds in reaction-diffusion equations with advection. (English) Zbl 1002.35069
The authors investigate the following question: which characteristic of the ambient fluid flow is responsible for burning rate enhancement? Note that the bulk burning rate \[ V(t)=\int_\Omega T_t(x,y,t) {dxdy \over H} \] and its time average \[ \langle V\rangle_t={1\over t}\int^t_0 V(s)ds, \] where \(T\) denotes the temperature, satisfy the corresponding PDE. Here they consider a general class of reaction rates \(f(T)\) that are either of the ignition or general KPP type, and establish lower bounds for \(V(t)\) for percolating flows that are periodic in space. Another interesting result of the paper concerns cellular flows with closed streamlines.

MSC:
35K57 Reaction-diffusion equations
80A32 Chemically reacting flows
35K40 Second-order parabolic systems
35B45 A priori estimates in context of PDEs
35B10 Periodic solutions to PDEs
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