caa a22 4500 477091482 CHVBK 20180405111516.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF01194067 doi (NATIONALLICENCE)springer-10.1007/BF01194067 On symmetric and nonsymmetric blowup for a weakly quasilinear heat equation [Elektronische Daten] [Jerry Bebernes, Alberto Bressan, Victor Galaktionov] We construct blow-up patterns for the quasilinear heat equation (QHE) $$u_t = \nabla \cdot (k(u)\nabla u) + Q(u)$$ in Ω×(0,T), Ω being a bounded open convex set in ℝ N with smooth boundary, with zero Dirichet boundary condition and nonnegative initial data. The nonlinear coefficients of the equation are assumed to be smooth and positive functions and moreoverk(u) andQ(u)/u p with a fixedp>1 are of slow variation asu→∞, so that (QHE) can be treated as a quasilinear perturbation of the well-known semilinear heat equation (SHE) $$u_t = \nabla u) + u^p .$$ We prove that the blow-up patterns for the (QHE) and the (SHE) coincide in a structural sense under the extra assumption $$\smallint ^\infty k(f(e^s ))ds = \infty ,$$ wheref(v) is a monotone solution of the ODEf′(v)=Q(f(v))/v p defined for allv≫1. If the integral is finite then the (QHE) is shown to admit an infinite number of different blow-up patterns. Birkhäuser Verlag, 1996 Bebernes Jerry Program in Applied Mathematics, University of Colorado, 80309-0526, Boulder, Colorado, USA aut Bressan Alberto S.I.S.S.A., Via Beirut 4, 34013, Trieste, Italy aut Galaktionov Victor Department of Mathematics, Universidad Autonoma de Madrid, 28049, Madrid, Spain aut Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/3(1996-09-01), 269-286 1021-9722 3:3<269 1996 3 30 https://doi.org/10.1007/BF01194067 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01194067 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bebernes Jerry Program in Applied Mathematics, University of Colorado, 80309-0526, Boulder, Colorado, USA aut NATIONALLICENCE 700 1- Bressan Alberto S.I.S.S.A., Via Beirut 4, 34013, Trieste, Italy aut NATIONALLICENCE 700 1- Galaktionov Victor Department of Mathematics, Universidad Autonoma de Madrid, 28049, Madrid, Spain aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/3(1996-09-01), 269-286 1021-9722 3:3<269 1996 3 30 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer