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- W2018017658 abstract "In this paper, the Cauchy problem of the system $$u_{1,t} = Delta u_{1} - u_1 u_2^{m}, quad u_{2,t} = d Delta u_2 + u_1 u_2^{m}$$ is studied, where x ∈ R2, m ≥ 1 and d > 0 is the Lewis number. This system models isothermal combustion (see [7]), and auto-catalytic chemical reaction. We show the global existence and regularity of solutions with non-negative initial values having mild decay as |x| → ∞. More importantly, we establish the exact spatio-temporal profiles for such solutions. In particular, we prove that for m = 1, the exact large time behavior of solutions is characterized by a universal, non-Gaussian spatio-temporal profile, with anomalous exponents, due to the fact that quadratic nonlinearity is critical in 2D. Our approach is a combination of iteration using Renormalization Group method, which has been developed into a very powerful tool in the study of nonlinear PDEs largely by the pioneering works of Bricmont, Kupiainen and Lin [6], Bricmont, Kupiainen and Xin, [7], (see also [9]) and key..." @default.
- W2018017658 created "2016-06-24" @default.
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- W2018017658 date "2006-04-01" @default.
- W2018017658 modified "2023-10-16" @default.
- W2018017658 title "DYNAMICS AND UNIVERSALITY OF AN ISOTHERMAL COMBUSTION PROBLEM IN 2D" @default.
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- W2018017658 doi "https://doi.org/10.1142/s0129055x06002681" @default.
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