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Gradient blowup rate for a viscous Hamilton-Jacobi equation with degenerate diffusion. (English) Zbl 1264.35060
Summary: This paper is concerned with the gradient blowup rate for the one-dimensional $p$-Laplacian parabolic equation $u_t=(\vert u_x\vert^{p-2}u_x)_x+\vert u_x\vert^q$ with $q>p>2$, for which the spatial derivative of solutions becomes unbounded in finite time while the solutions themselves remain bounded. We establish the blowup rate estimates of lower and upper bounds and show that in this case the blowup rate does not match the self-similar one.

MSC:
35B44Blow-up (PDE)
35B20Perturbations (PDE)
35K51Second-order parabolic systems, initial bondary value problems
35B40Asymptotic behavior of solutions of PDE
35K92Quasilinear parabolic equations with $p$-Laplacian
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Full Text: DOI
References:
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