کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
844270 908582 2007 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Asymptotics in the critical case for Whitham type equations
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Asymptotics in the critical case for Whitham type equations
چکیده انگلیسی

Consider the Cauchy problem for nonlinear dissipative evolution equations {ut+N(u,u)+Lu=0,x∈R,t>0,u(0,x)=u0(x),x∈R, where LL is the linear pseudodifferential operator Lu=F¯ξ→x(L(ξ)û(ξ)) and the nonlinearity is a quadratic pseudodifferential operator N(u,u)=F¯ξ→x∫RA(t,ξ,y)û(t,ξ−y)û(t,y)dy,û≡Fx→ξu is direct Fourier transformation. Let the initial data u0∈Hβ,0∩H0,β, β>12, are sufficiently small and have a non-zero total mass M=∫u0(x)dx≠0, here Hn,m={ϕ∈L2‖〈x〉m〈i∂x〉nϕ(x)‖L2<∞} is the weighted Sobolev space. Then we prove that the main term of the large time asymptotics of solutions in the critical case is given by the self-similar solution defined uniquely by the total mass MM of the initial data.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 67, Issue 10, 15 November 2007, Pages 2914–2933
نویسندگان
, , ,