TY - JOUR
T1 - On a class of thermal blow-up patterns
AU - Levy, Doron
AU - Rosenau, Philip
N1 - Funding Information:
The authors are grateful to Mr. A. Kurganov for a number of illuminative observations and to Ms. R. Moses for her help with the numerics of the 1D problem. This work was supported in part by a grant from the Israel Science Foundation.
PY - 1997/12/22
Y1 - 1997/12/22
N2 - We study the patterns of a thermal explosion as described via u1 = (Δ + 1)um, m > 1. These processes, characterized by an intrinsic length scale, always converge into very simple, universal, space-time separable, axisymmetric pattern(s) with a compact support - referred to as dissipative compactons. When the initial datum is specified on an axisymmetric annulus, though the evolving pattern seems to preserve this symmetry, at a later stage, it collapses very quickly to the center. In a perturbed annulus, local axisymmetric patches of blow-up form instead of a collapse. For a planar, homogeneous, Dirichlet problem, the space-time separability of the emerging pattern is preserved as well, but the competition between the intrinsic and extrinsic characteristic scales generates a wider variety of spatial patterns, with the self-localization taking place on large domains. As the width of the domain diminishes, then depending on the width-length ratio, the emerging pattern first partially, and then fully, attaches to the boundaries. With further decrease of the domain, the emerging separable pattern, instead of exploding, decays algebraically in time.
AB - We study the patterns of a thermal explosion as described via u1 = (Δ + 1)um, m > 1. These processes, characterized by an intrinsic length scale, always converge into very simple, universal, space-time separable, axisymmetric pattern(s) with a compact support - referred to as dissipative compactons. When the initial datum is specified on an axisymmetric annulus, though the evolving pattern seems to preserve this symmetry, at a later stage, it collapses very quickly to the center. In a perturbed annulus, local axisymmetric patches of blow-up form instead of a collapse. For a planar, homogeneous, Dirichlet problem, the space-time separability of the emerging pattern is preserved as well, but the competition between the intrinsic and extrinsic characteristic scales generates a wider variety of spatial patterns, with the self-localization taking place on large domains. As the width of the domain diminishes, then depending on the width-length ratio, the emerging pattern first partially, and then fully, attaches to the boundaries. With further decrease of the domain, the emerging separable pattern, instead of exploding, decays algebraically in time.
UR - http://www.scopus.com/inward/record.url?scp=0041165389&partnerID=8YFLogxK
U2 - 10.1016/S0375-9601(97)00768-8
DO - 10.1016/S0375-9601(97)00768-8
M3 - מאמר
AN - SCOPUS:0041165389
VL - 236
SP - 483
EP - 493
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
SN - 0375-9601
IS - 5-6
ER -