Dependence of the blow‐up time with respect to parameters and numerical approximations for a parabolic problem

Article type: Research Article

Authors: Groisman, Pablo^; | Rossi, Julio D.^;

Affiliations: Instituto de Calculo, FCEyN, UBA (1428) Pab. II, Ciudad Universitaria, Buenos Aires, Argentina E‐mail: pgroisma@dm.uba.ar | Departamento de Matemática, FCEyN, UBA (1428) Buenos Aires, Argentina E‐mail: jrossi@dm.uba.ar

Note: [] Corresponding author.

Note: [] Current address: Departamento de Matemática, Universidad Católica de Chile, casilla 306, correo 22, Santiago, Chile. E‐mail: jrossi@mat.puc.cl.

Abstract: We find a bound for the modulus of continuity of the blow‐up time for the problem ut=λΔu+up, with initial datum u(x,0)=ϕ(x)+hf(x) respect to the parameters λ, p and h. We also find an estimate for the rate of convergence of the blow‐up times for a semi‐discrete numerical scheme.

Keywords: blow‐up, semilinear parabolic equations, semidiscretization in space

Journal: Asymptotic Analysis, vol. 37, no. 1, pp. 79-91, 2004