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Rate estimates of gradient blowup for a heat equation with exponential nonlinearity. (English) Zbl 1189.35033

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:

35B44 Blow-up in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35K58 Semilinear parabolic equations
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