Direct and inverse source problems for degenerate parabolic equations
نویسندگان
چکیده
منابع مشابه
global results on some nonlinear partial differential equations for direct and inverse problems
در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
Inverse problems for parabolic equations
Let ut −∇2u = f(x) := ∑M m=1 amδ(x− xm) in D × [0,∞), where D ⊂ R3 is a bounded domain with a smooth connected boundary S, am = const, δ(x− xm) is the delta-function. Assume that u(x, 0) = 0, u = 0 on S. Given the extra data u(yk, t) := bk(t), 1 ≤ k ≤ K, can one find M,am, and xm? Here K is some number. An answer to this question and a method for finding M,am, and xm are given.
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This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source xut − (xux)x = ∫ a 0 u pdx in (0, a) × (0, T ) subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in fini...
متن کاملOn Degenerate Parabolic Equations
Mohammed Kbiri Alaoui Department of Mathematics, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia Correspondence should be addressed to Mohammed Kbiri Alaoui, mka [email protected] Received 31 March 2011; Accepted 28 July 2011 Academic Editor: Mihai Putinar Copyright q 2011 Mohammed Kbiri Alaoui. This is an open access article distributed under the Creative Commons Attribution License, which...
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This article presents a mathematical analysis of input–output mappings in inverse coefficient and source problems for the linear parabolic equation ut = (k(x)ux)x + F(x, t), (x, t) ∈ ΩT := (0,1) × (0, T ]. The most experimentally feasible boundary measured data, the Neumann output (flux) data f (t) := −k(0)ux(0, t), is used at the boundary x = 0. For each inverse problems structure of the input...
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ژورنال
عنوان ژورنال: Journal of Inverse and Ill-posed Problems
سال: 2020
ISSN: 1569-3945,0928-0219
DOI: 10.1515/jiip-2019-0046