Inverse heat problem of determining time-dependent source parameter in reproducing kernel space

Nonlinear Analysis: Real World Applications - Tập 14 - Trang 875-887 - 2013
Wenyan Wang1, Bo Han1, Masahiro Yamamoto2
1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
2Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo 153-8914, Japan

Tài liệu tham khảo

Dehghan, 2001, An inverse problem of finding a source parameter in a semilinear parabolic equation, Appl. Math. Model., 25, 743, 10.1016/S0307-904X(01)00010-5 Cannon, 1991, On a class of nonlinear parabolic equations with nonlinear trace type functionals, Inverse Problems, 7, 149, 10.1088/0266-5611/7/1/014 Ai, 2010, On the inverse scattering problem and the low regularity solutions for the Dullin–Gottwald–Holm equation, Nonlinear Anal. RWA, 11, 888, 10.1016/j.nonrwa.2009.01.031 Baran, 2005, Numerical procedures for determining of an unknown parameter in parabolic equation, Appl. Math. Comput., 162, 1219, 10.1016/j.amc.2004.03.003 Dehghan, 2005, Parameter determination in a partial differential equation from the overspecified data, Math. Comput. Modelling, 41, 197, 10.1016/j.mcm.2004.07.010 Cannon, 1994, Numerical procedures for the determination of an unknown coefficient in semi-linear parabolic differential equations, Inverse Problems, 10, 227, 10.1088/0266-5611/10/2/004 Cannon, 1990, An inverse problem of finding a parameter in a semi-linear heat equation, J. Math. Anal. Appl., 145, 470, 10.1016/0022-247X(90)90414-B Cannon, 1992, Determination of source parameter in parabolic equations, Meccanica, 27, 85, 10.1007/BF00420586 Liu, 2011, Global uniqueness and stability in determining the damping and potential coefficients of an inverse hyperbolic problem, Nonlinear Anal. RWA, 12, 1562, 10.1016/j.nonrwa.2010.10.014 Prilepko, 1987, Solvability of the inverse boundary value problem of finding a coefficient of a lower order term in a parabolic equation, J. Differential Equations, 23, 136 MacBain, 1986, Existence and uniqueness properties for one-dimensional magnetotellurics inversion problem, J. Math. Phys., 27, 645, 10.1063/1.527219 MacBain, 1987, Inversion theory for a parametrized diffusion problem, SIAM J. Appl. Math., 47, 1386, 10.1137/0147091 Wang, 1989, A finite difference solution to an inverse problem determining a control function in a parabolic partial differential equation, Inverse Problems, 5, 631, 10.1088/0266-5611/5/4/013 Tuan, 2011, Two regularization methods for backward heat problems with new error estimates, Nonlinear Anal. RWA, 12, 1720, 10.1016/j.nonrwa.2010.11.004 Yousefi, 2009, Legendre multiscaling functions for solving the one-dimensional parabolic inverse problem, Numer. Methods Partial Differential Equations, 25, 1502, 10.1002/num.20430 Yang, 2010, Numerical method for the simultaneous determination of unknown parameters in a parabolic equation, Int. J. Comput. Math., 87, 150, 10.1080/00207160801979199 Cheng, 2008, Determination of a control parameter in a one-dimensional parabolic equation using the moving least-square approximation, Int. J. Comput. Math., 85, 1363, 10.1080/00207160701481429 Johansson, 2008, A procedure for determining a spacewise dependent heat source and the initial temperature, Appl. Anal., 87, 265, 10.1080/00036810701858193 Johansson, 2010, A method for identifying a spacewise-dependent heat source under stochastic noise interference, Inverse Probl. Sci. Eng., 18, 51, 10.1080/17415970903233960 Fatullayev, 2001, Numerical procedure for the determination of an unknown parameter in a parabolic equation, Int. J. Comput. Math., 78, 103, 10.1080/00207160108805099 Dehghan, 2005, Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement, Numer. Methods Partial Differential Equations, 21, 611, 10.1002/num.20055 Fatullayev, 2000, Numerical procedures for determining unknown source parameter in parabolic equations, Math. Comput. Simul., 54, 159, 10.1016/S0378-4754(00)00221-4 Shaw, 2009, Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks, Internat. J. Non-Linear Mech., 44, 417, 10.1016/j.ijnonlinmec.2009.02.002 Lin, 2005, Representation of the exact solution for infinite system of linear equations, Appl. Math. Comput., 168, 636, 10.1016/j.amc.2004.09.025 Liew, 2002, Meshfree method for large deformation analysis-a reproducing kernel particle approach, Eng. Struct., 24, 543, 10.1016/S0141-0296(01)00120-1 Shaw, 2007, Reproducing kernel collocation method applied to the non-linear dynamics of pipe whip in a plane, Int. J. Impact Eng., 34, 1637, 10.1016/j.ijimpeng.2006.09.004 Antoniou, 1999, Wavelets and stochastic processes, Math. Comput. Simul., 49, 81, 10.1016/S0378-4754(99)00009-9 Hult, 2003, Approximating some Volterra type stochastic integrals with applications to parameter estimation, Stoch. Proc. Appl., 105, 1, 10.1016/S0304-4149(02)00250-8 Xian, 2006, Weighted sampling and signal reconstruction in spline subspaces, Signal Process., 86, 331, 10.1016/j.sigpro.2005.05.013 Pontil, 2003, A note on different covering numbers in learning theory, J. Complexity, 19, 665, 10.1016/S0885-064X(03)00033-5 Takeuchi, 2008, Tikhonov regularization by a reproducing kernel Hilbert space for the Cauchy problem for an elliptic equation, SIAM J. Sci. Comput., 31, 112, 10.1137/070684793 Hon, 2011, Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem, Adv. Comput. Math., 34, 167, 10.1007/s10444-010-9148-1 Saitoh, 2001, Applications of the reproducing kernel theory to inverse problems, Comm. Korean Math. Soc., 16, 371 Aronszajn, 1950, Theory of reproducing kernels, Trans. Amer. Math. Soc., 68, 1, 10.1090/S0002-9947-1950-0051437-7 Saitoh, 1988 Cui, 2009 Alpay, 2004, Carathéodory Fejér interpolation in the ball with mixed derivatives, Linear Algebra Appl., 382, 117, 10.1016/j.laa.2003.11.029 Alpay, 2002, The Schur algorithm and reproducing kernel Hilbert spaces in the ball, Linear Algebra Appl., 342, 163, 10.1016/S0024-3795(01)00448-7 Wasilkowski, 2004, Finite-order weights imply tractability of linear multivariate problems, J. Approx. Theory, 130, 57, 10.1016/j.jat.2004.06.011 Xu, 2001, Representation of reproducing kernels and the Lebesgue constants on the ball, J. Approx. Theory, 112, 295, 10.1006/jath.2001.3597 Fasshauer, 2005, Dual bases and discrete reproducing kernels: a unified framework for RBF and MLS approximation, Eng. Anal. Bound. Elem., 29, 313, 10.1016/j.enganabound.2004.05.007 Luo, 1998, Error estimates and convergence rates for variational Hermite interpolation, J. Approx. Theory, 95, 264, 10.1006/jath.1997.3218 Christensen, 2005, The finite section method and problems in frame theory, J. Approx. Theory, 133, 221, 10.1016/j.jat.2005.01.001 Cui, 2007, A computational method for solving one-dimensional variable-coefficient Burgers equation, Appl. Math. Comput., 188, 1389, 10.1016/j.amc.2006.11.005 Zhou, 2009, Numerical algorithm for parabolic problems with non-classical conditions, J. Comput. Appl. Math., 230, 770, 10.1016/j.cam.2009.01.012 Prilepko, 2000