An inverse heat conduction problem with a nonlinear source term

Inverse Estimation of the Initial Condition for the Heat Equation

“…For the direct problem where the initial condition f (x) is specified, the problem given by equation (1)(2)(3)(4) is concerned with the determination of the temperature distribution u(x, t) in the interior region of the solid as a function of time and position.…”

“…Inverse heat conduction problems have many applications in various branches of science and engineering,mechanical and chemical engineers, mathematicians and specialists in many other sciences branches are interested in inverse problems (see [1,2,3,4,5]),each with different application in mind. The main difficulty in the treatment of inverse problems is the instability of their solution in the presence of noise in the observed (measured) data, that is, the ill-posed nature Received: September 11, 2012 c 2013 Academic Publications, Ltd.…”

Estimation of unknown heat source function in inverse heat conduction problems using quantum-behaved particle swarm optimization

“…The inverse problem of determining an unknown heat source has been investigated in many papers [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In [12], temperature measurements on the whole domain are required to get the solution of the inverse heat source problem, which is usually impractical in engineering.…”

“…A frequent used technique to study inverse problems is the nonlinear least-squares method which minimizes the difference between the experimental measurements and the calculated responses of the system. In solving this problem, several approaches have been adopted such as conjugate gradient method [10,14], Davidson-Fletcher-Powell method, the MonteCarlo technique, covariance analysis and dynamic programming, which all require the gradient computation. It is well known that the gradient based methods converge fast but the gradient computation is sometimes complicated and the convergence depends strongly on the choice of initial guess of the unknown function.…”

Properties and optimality conditions of a three-dimension non-smooth thermodynamic system of sea ice

“…In recent years, there are many researchers devoting to the parameter identification problems of thermodynamic systems. Some researchers [9][10][11][12] considered the determination of source terms, some researchers [13][14][15] considered the determination of thermal conductivities.…”