A problem of coefficient determination in parabolic equations solved as moment problem

  • Abstract
  • Keywords
  • References
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  • 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.

  • Keywords

    Generalized Moment Problem;Integral Equations;Inverse Problem;Parabolic Pdes;Truncated Expansion Method.

  • References

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Article ID: 8319
DOI: 10.14419/ijamr.v6i4.8319

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