کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
840251 | 1470517 | 2013 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Second-order differential equations on R+ governed by monotone operators
دانلود مقاله + سفارش ترجمه
دانلود مقاله ISI انگلیسی
رایگان برای ایرانیان
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
سایر رشته های مهندسی
مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Consider in a real Hilbert space H the differential equation (E):p(t)uâ²â²(t)+q(t)uâ²(t)âAu(t)+f(t), for a.a. tâR+=[0,â), with the condition u(0)=xâD(A)¯, where A:D(A)âHâH is a (possibly set-valued) maximal monotone operator, with [0,0]âA (or, more generally, 0âR(A)); p,qâLâ(R+), with essinfp>0 and either essinfq>0 or esssupq<0. Recall that equation (E) in the case pâ¡1,qâ¡0,fâ¡0, subject to u(0)=x and suptâ¥0âu(t)â<â, was investigated in the early 1970s by V. Barbu, who derived in particular from his results a definition for the square root of the nonlinear operator A. Subsequently H. Brézis, N.H. Pavel, L. Véron and others have paid attention to equation (E). In this paper we prove the existence and uniqueness of the solution to equation (E) subject to u(0)=xâD(A) in the weighted space X=Lb2(R+;H), where b(t)=a(t)/p(t), a(t)=exp(â«0tq(s)/p(s)ds), under our weak assumptions on p and q (see above) and fâX. For xâD(A)¯ we prove the existence of a generalized solution. This is a classic solution if pâ¡1, qâ¡câRâ{0}. If pâ¡1,q(t)â¡câRâ{0}, fâ¡0 the solutions give rise to a nonlinear semigroup of contractions. If A is linear its infinitesimal generator G is given by G=â(c/2)Iâ(c2/4)I+A.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 83, May 2013, Pages 69-81
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 83, May 2013, Pages 69-81
نویسندگان
Gheorghe MoroÅanu,