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In this paper, we first discuss a representation of solutions to the initial value problem and the initial-boundary value problem for discrete evolution equations $$ \sum_{n=0}^l c_n \partial_t^n u(x,t)-\rho(x)\Delta_\omega u(x,t)=H(x,t), $$ defined on networks, i.e. on weighted graphs. Secondly, we show that the weight of each link of networks can be uniquely identified by using their Dirichlet data and Neumann data on the boundary, under a monotonicity condition on their weights.
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참고문헌 (14)
참고문헌 신청
G. Alessandrini / 1989 / Remark on a paper by H. Bellout and A. Friedman / Boll. Un. Mat. Ital. A 3(7):243~249
E. Bendito / 2005 / Potential theory for Schr¨odinger operators on finite networks / Rev. Mat. Iberoamericana 21(3):771~813
E. Bendito / 2007 / Potential theory for boundary value problems on finite networks / Appl. Anal. Discrete Math 1(1):299~310
F. R. K. Chung / 1997 / Spectral Graph Theory / CBMS Regional Conference Series in Math 92
F. R. K. Chung / 2000 / Discrete Green’s functions / J. Combin. Theory Ser. A 9(1-2):191~214
E. Bendito / 2005 / Potential theory for Schr¨odinger operators on finite networks / Rev. Mat. Iberoamericana 21(3):771~813
E. Bendito / 2007 / Potential theory for boundary value problems on finite networks / Appl. Anal. Discrete Math 1(1):299~310
F. R. K. Chung / 1997 / Spectral Graph Theory / CBMS Regional Conference Series in Math 92
F. R. K. Chung / 2000 / Discrete Green’s functions / J. Combin. Theory Ser. A 9(1-2):191~214
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