
Summary: For a wide class of nonlinear parabolic equations of the form \(u_t-\Delta u=F(u, \nabla u)\), we give finite time blow-up results for large initial data. Blow-up time estimates are also provided. These results rely on a new method of comparison with suitable blowing up self-similar subsolutions. As a consequence, we improve several known results on reaction-diffusion equations, on generalized Burgers' equations and on the equation of Chipot and Weissler. This method can also apply to degenerate equations of porous medium type, and provides a unified treatment for a large class of problems, both semilinear and quasilinear.
blow up times, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Asymptotic behavior of solutions to PDEs, Applied Mathematics, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, large initial data, Maximum principles in context of PDEs, degenerate equations of porous medium type, equation of Chipot and Weissler, Nonlinear parabolic equations, gradient term, generalized Burgers' equations, Stability in context of PDEs, Analysis
blow up times, Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations, Asymptotic behavior of solutions to PDEs, Applied Mathematics, Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs, large initial data, Maximum principles in context of PDEs, degenerate equations of porous medium type, equation of Chipot and Weissler, Nonlinear parabolic equations, gradient term, generalized Burgers' equations, Stability in context of PDEs, Analysis
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