Traveling curved fronts in the buffered bistable systems in \(\mathbb{R}^2\). (English) Zbl 1491.35113
Summary: We consider traveling curved fronts in the buffered bistable systems in \(\mathbb{R}^2\) and show that multiple stationary buffers (where buffers do not diffuse) cannot prevent the existence of V-shaped calcium concentration waves. In other words, for the buffered bistable systems we prove that there exist V-shaped traveling fronts in \(\mathbb{R}^2\) by constructing the proper supersolution and subsolution, applying the comparison principle and the fixed point theory.
MSC:
| 35C07 | Traveling wave solutions |
| 35B51 | Comparison principles in context of PDEs |
| 35K40 | Second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
Keywords:
buffered bistable systems; traveling curved fronts; comparison principle; existence; supersolution; subsolutionReferences:
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