The Optimal Stability Estimate for some Ill-posed Cauchy Problems for a Parabolic Equation (original) (raw)

Abstract

A u $ m r g , West Germany and Sergio Vessella l.sri!uio Anu1i.d Gkahule e Applicazioni, Viu Santa Marta 13/A, 1-20139 Firenze, Italy Communicated by L. E. Payne In this paper we consider the non-characteristic Cauchy problem U,-a(x)u,,-h(x)u,-c(x)u=O, x ~ (0 , I), r e / , u(O,t)=cp(t), u,(O,t)=O, t E I , where I = iw or I = R', and u(x,O)=O, x ~ [ O , l ] , in the case I = R +. Assuming an a priori bound for (1 U([, .) 111~2, we derive the exact Holder type dependence of 11 u(x, .) lll. l on I 1 cp Ill.2

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References (7)

  1. Cannon, J. R., 'A Cauchy problem for the heat equation,' Ann. Mac. Pura e Appl. ( I V ) , LXVI, 155-166, (1964).
  2. Knabner, P. and Vessella, S., 'Stability estimates for ill-posed Cauchy problems for parabolic equations,' in Engl, H. W. and Groetsch, C. W. (eds), Inverse and Ill-posed Problems, Academic Press, New York,
  3. Knabner, P. and Vessella, S., 'Stabilization of ill-posed Cauchy problems for parabolic equations,' Ann.
  4. Manselli, P. and Miller, K., 'Calculation of the surface temperature and heat flux on one side of a wall
  5. Payne, L., 'Improved stability estimates for classes of ill-posed Cauchy problems,' Appl. Anal., 19,63-74,
  6. Pucci, C., 'Alcune limitazioni per le soluzioni di equazioni paraboliche,' Ann. Mar. Pura e Appl. ( I V ) , 1987 pp. 351-368.
  7. Mat. Pura e Appl. (IV), CIL, 383409 (1987). from measurements on the opposite side,' Ann. Mat. Pura e Appl. ( I V ) , CXXIII, 161-183, (1980). (1985h XLVIII, 161-172, (1959).