کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5775204 | 1413578 | 2017 | 13 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Elliptic-like regularization of semilinear evolution equations and applications to some hyperbolic problems
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Elliptic-like regularization of semilinear evolution equations and applications to some hyperbolic problems Elliptic-like regularization of semilinear evolution equations and applications to some hyperbolic problems](/preview/png/5775204.png)
چکیده انگلیسی
Consider in a Hilbert space H the Cauchy problem (P0): uâ²(t)+Au(t)+Bu(t)=f(t), 0â¤tâ¤T; u(0)=u0, where A:D(A)âHâH is the generator of a C0-semigroup of contractions and B:HâH is Lipschitzian on bounded sets and monotone. Following the method of artificial viscosity introduced by J.L. Lions, we associate with (P0) the approximate problem (Pε): âεuâ³(t)+uâ²(t)+Au(t)+Bu(t)=f(t), 0â¤tâ¤T; u(0)=u0, u(T)=uT, where ε is a positive small parameter. We establish an asymptotic expansion of the solution uε of (Pε), showing that uε corrected by a boundary layer function approximates the solution of (P0) with respect to the sup norm of C([0,T];H). The same asymptotic expansion still holds if B is not necessarily monotone but is Lipschitzian on H. This paper is a significant extension of a previous one by M. Ahsan and G. MoroÅanu [2] so that the framework created here allows the treatment of hyperbolic problems (besides parabolic ones). Specifically, our main result is illustrated with the semilinear telegraph system (thus extending a result by N.C. Apreutesei and B. Djafari Rouhani [3]) and the semilinear wave equation.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 2, 15 May 2017, Pages 966-978
Journal: Journal of Mathematical Analysis and Applications - Volume 449, Issue 2, 15 May 2017, Pages 966-978
نویسندگان
LuminiÅ£a Barbu, Gheorghe MoroÅanu,