International Journal of Mathematics and Computers in Simulation. Vol.5, No.4 (2011), 318-325
Suggested Citation
Panumart Sawangtong, Wannika Jumpen Complete blow-up for a degenerate semilinear parabolic problem in the sense of semigroup theory. International Journal of Mathematics and Computers in Simulation. Vol.5, No.4 (2011), 318-325. Retrieved from: https://repository.li.mahidol.ac.th/handle/123456789/11791
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Complete blow-up for a degenerate semilinear parabolic problem in the sense of semigroup theory
Before blow-up occurs, under certain conditions, we establish a unique blow-up solution for a degenerate semilinear parabolic problem: u t - (a(x)u x ) x = f (u) in (0,1) × (0, ∞) where f is a specified function and a(0) = 0, a(x) > 0 on (0,1] together with the Dirichlet boundary condition and the suitable initial condition. The blow-up set of such a blow-up solution u is given. Furthermore, the sufficient condition to guarantee the occurrence for blow-up in finite time is shown.
