Blow-up in semilinear parabolic equations with weak diffusion

References

• Bebernes , J and Bricher , S . 1992 . Final time blow-up profiles for semilinear parabolic equations via centre manifold theory . SIAM J. Appl. Math. , 23 : 852 – 69 .
   Google Scholar
• Bebernes , J and Eberly , D . 1989 . Mathematical Problems for Combustion Theory , Berlin : Springer .
   Google Scholar
• Bebernes , J and Kassoy , D R . 1988 . “ Characterizing self-similar blow-up ” . In Mathematical Modelling of Combustion and Related Topics , Edited by: Brauner , C M and Schmidt-Laine , C . 383 – 92 . Dordrecht : Nijhoff .
   Google Scholar
• Bebernes , J and Troy , W . 1987 . On the existence of solutions to the Kassoy problem in dimension 1 . SIAM J. Math. Anal. , 18 : 1157 – 62 .
   Google Scholar
• Berger , M and Kohn , R V . 1988 . A rescaling algorithm for the numerical calculation of blowing-up solutions . Commun. Pure Appl. Math. , 41 : 841 – 63 .
   Web of Science ®Google Scholar
• Blythe , P A and Crighton , D G . 1989 . Shock generated ignition: the induction zone . Proc. R. Soc.A , 426 : 189 – 209 .
   Google Scholar
• Budd , C J , Dold , J W and Galaktionov , V A . 1993 . Self-similar solutions of a quasilinear diffusion problem . Adv. Diff. Eq. , to appear
   Google Scholar
• Budd , C J , Huang , W H and Russell , R D . 1996 . Moving mesh methods for problems with blow-up . SIAM J. Sci. Comput. , 17 : 305 – 27 .
   Web of Science ®Google Scholar
• Dold , J W . 1985 . Analysis of the early stage of thermal runaway . Quart. J. Mech. Appl. Math. , 38 : 361 – 87 .
   Web of Science ®Google Scholar
• Dold , J W . 1988 . “ Dynamic transition of a self-igniting region ” . In Mathematical Modelling of Combustion and Related Topics , Edited by: Brauner , C M and Schmidt-Laine , C . 461 – 70 . Dordrecht : Nijhoff .
   Google Scholar
• Dold , J W . 1991 . On asymptotic forms of reactive diffusive runaway . Proc. R. Soc.A , 433 : 521 – 45 .
   Google Scholar
• Filippas , S and Kohn , R . 1992 . Refined asymptotics for the blow up of ut,+Δu=up Commun . Pure Appl. Math. , 45 : 821 – 69 .
   Web of Science ®Google Scholar
• Friedman , A and Lacey , A A . 1987 . The blow-up time for solutions of nonlinear heat equations with small diffusion . SIAM J. Math. Anal. , 18 : 711 – 21 .
   Web of Science ®Google Scholar
• Galaktionov , V A and Posashkov , S A . 1991 . Single point blow-up for N,-dimensional quasilinear equations with gradient diffusion and source . Indiana Univ. Math. J. , 40 : 1041 – 60 .
   Web of Science ®Google Scholar
• Herrero , M and Velaquez , J . 1993 . Blow-up behaviour for one-dimensional semilinear parabolic equations . Ann. Inst. H Poincare, Analyse nonlineaire , 10 : 131 – 89 .
   Web of Science ®Google Scholar
• Jackson , T L , Kapila , A K and Stewart , D S . 1989 . Evolution of a reaction center in an explosive material . SIAM J. Appl. Math. , 49 : 432 – 58 .
   Web of Science ®Google Scholar
• Kapila , A K . 1980 . Reactive-diffusive system with Arrhenius kinetics: dynamics of ignition . SIAM J. Appl. Math. , 39 : 21 – 36 .
   Web of Science ®Google Scholar
• Kassoy , D and Poland , J . 1980 . The thermal explosion Confined by a constant temperature boundary: I. The induction period solution . SIAM J. Appl. Math. , 39 : 412 – 30 .
   Web of Science ®Google Scholar
• Lacey , A A . 1981 . The spatial dependence of supercritical reacting systems . IMA J. Appl. Maths. , 27 : 71 – 84 .
   Web of Science ®Google Scholar
• Short , M . 1997 . On the critical conditions for the initiation of detonation in a non-uniformly perturbed reactive fluid . SIAM J. Appl. Math. , 57 : 1242 – 80 .
   Web of Science ®Google Scholar