کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
6417035 1338514 2016 24 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Lifespan of solutions to the damped wave equation with a critical nonlinearity
ترجمه فارسی عنوان
طول عمر راه حل معادله موج خنثی با یک غیر خطی بحرانی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
چکیده انگلیسی

In the present paper, we study a lifespan of solutions to the Cauchy problem for semilinear damped wave equations(DW){∂t2u−Δu+∂tu=f(u),(t,x)∈[0,T(ε))×Rn,u(0,x)=εu0(x),x∈Rn,∂tu(0,x)=εu1(x),x∈Rn, where n≥1, f(u)=±|u|p−1u or |u|p, p≥1, ε>0 is a small parameter, and (u0,u1) is a given initial data. The main purpose of this paper is to prove that if the nonlinear term is f(u)=|u|p and the nonlinear power is the Fujita critical exponent p=pF=1+2n, then the upper estimate to the lifespan is estimated byT(ε)≤exp⁡(Cε−p) for all ε∈(0,1] and suitable data (u0,u1), without any restriction on the spatial dimension. Our proof is based on a test-function method utilized by Zhang [35]. We also prove a sharp lower estimate of the lifespan T(ε) to (DW) in the critical case p=pF.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 261, Issue 3, 5 August 2016, Pages 1880-1903
نویسندگان
, ,