Abstract
We study finite time quenching for heat equations coupled via singular nonlinear boundary flux. A criterion is proposed to identify the simultaneous and non-simultaneous quenchings. In particular, three kinds of simultaneous quenching rates are obtained for different nonlinear exponent regions and appropriate initial data. This extends an original work by Pablo, Quirós and Rossi for a heat system with coupled inner absorption terms subject to homogeneous Neumann boundary conditions.
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This work was supported by the National Natural Science Foundation of China (Grant No. 10471013, 10771024)
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Zheng, S., Song, X. Quenching rates for heat equations with coupled singular nonlinear boundary flux. Sci. China Ser. A-Math. 51, 1631–1643 (2008). https://doi.org/10.1007/s11425-007-0178-1
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DOI: https://doi.org/10.1007/s11425-007-0178-1
Keywords
- quenching
- simultaneous quenching
- non-simultaneous quenching
- quenching rate
- heat equation
- singular nonlinear boundary flux