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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.

35B44Blow-up (PDE)
35B40Asymptotic behavior of solutions of PDE
35K58Semilinear parabolic equations
Full Text: DOI
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