Abstract
The problem is to find a(t) y w(x; t) such that wt = a(t) (wx)x+r(x; t) under the initial condition w(x; 0) =fi(x) and the boundary conditions w(0; t) = 0 ; wx(0; t) = wx(1; t)+alfa w(1; t) about a region D ={(x; t); 0 <x < 1; t >0}. In addition it must be fulfilled the integral of w (x, t) with respect to x is equal to E(t) where fi(x) , r(x; t) and E(t) are known functions and alfa is an arbitrary real number other than zero.The objective is to solve the problem as an application of the inverse moment problem. We will find an approximated solution and bounds for the error of the estimated solution using the techniques on moments problem. In addition, the method is illustrated with several examples.
Highlights
We want to find a(t) y w(x,t) such that uniqueness and continuously dependence upon the data of the classical solution are shown by using the generalized Fourier method”.wt = a(t)x + r(x,t) under the initial condition w(x, 0) = φ(x) and the boundary conditions w(0,t) = 0 wx(0,t) = wx(1,t) + αw(1,t)In general the methods applied to solve the problem are varied
(1) There is a great variety of inverse problems in which a parabolic equation must be solved and we must determine an unknown parameter[5, 6, 7], to name a few about a region D = {(x,t), 0 < x < 1, t > 0} In addition it must be fulfilled w(x,t)dx = E(t) where φ(x), r(x,t) and E(t) are known functions and α is an arbitrary real number other than zero
We assume that the underlying space is L2(D)
Summary
We want to find a(t) y w(x,t) such that uniqueness and continuously dependence upon the data of the classical solution are shown by using the generalized Fourier method”. Citing the abstract of this work: ”this paper investigates the inverse problem of simultaneously determining the time-dependent thermal diffusivity and the temperature distribution in a parabolic equation in the case of nonlocal boundary conditions containing a real parameter and integral overdetermination conditions, and under some consistency conditions on the input data the existence, The objective of this work is to show that we can solve the problem using the techniques of inverse moments problem. In a second step the following integral equation is solved in numerical form w∗(x,t)K(m, n, x,t)dxdt = ψ2(m, n) where w∗(x,t) it’s the unknown function, ψ2(m, n) is an expression in function of G(x,t) with K(m, n, x,t) known. Both integral equations are solved numerically by applying the moment problems techniques. We find an approximation for a(t) using a(t)w(1,t) and wAp(x,t)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Applied Mathematical Research
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
