Recovering the initial condition of parabolic equations from lateral Cauchy data via the quasi-reversibility method

摘要: We consider the problem of computing initial condition for a general parabolic equation from Cauchy lateral data. The stability this is well-known to be logarithmic. In paper, we introduce an approximate model, as coupled linear system elliptic partial differential equations. solution model vector Fourier coefficients solutions above. This solved by quasi-reversibility method. will prove convergence method measurement noise tends 0. convergent rate Lipschitz. present implementation our algorithm in details and verify showing some numerical examples.