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Zbl 1189.35033
Zhang, Zhengce; Hu, Bei
Rate estimates of gradient blowup for a heat equation with exponential nonlinearity. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 72, No. 12, 4594-4601 (2010). ISSN 0362-546X

Summary: We consider a one-dimensional semilinear parabolic equation $u_t = u_{xx}+\text e^{u_x}$, for which the spatial derivative of solutions becomes unbounded in finite time while the solutions themselves remain bounded. We establish estimates of blowup rate upper and lower bounds. We prove that in this case the blowup rate does not match the one obtained by the rescaling method.

MSC 2000:: *35B44
35B40 Asymptotic behavior of solutions of PDE
35K58

Keywords: one space dimension; nonlinear gradient source

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