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Gradient blowup solutions of a semilinear parabolic equation with exponential source

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  • In this paper, we consider the N-dimensional semilinear parabolic equation $ u_t=\Delta u+e^{|\nabla u|}$, for which the spatial derivative of solutions becomes unbounded in finite (or infinite) time while the solutions themselves remain bounded. We establish estimates of blowup rate as well as lower and upper bounds for the radial solutions. We prove that in this case the blowup rate does not match the one obtained by the rescaling method.
    Mathematics Subject Classification: Primary: 35K05, 35K35; Secondary: 35B40.


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