Abstract
Consider the problem where β > 0 and Ω = B R (0) ≔ x ∈ IRN; |x| < R. It is known ([AW]) that there is a positive number R o = R o (N,β) such that u exists globally if R < R o while for R> R o the solution u reaches zero in a finite time T (it quenches). The only point x o for which u(x o , t) → 0 as t 2192 T is x o = 0 (see [AK]).
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Fila, M., Hulshof, J., Quittner, P. (1992). The Quenching Problem on the N-dimensional Ball. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_14
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DOI: https://doi.org/10.1007/978-1-4612-0393-3_14
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