Approximating the Solution to the Cauchy Problem and the Boundary Value for the Laplace Equation
In this paper it is proved that the Cauchy problem and a boundary value problem for the Laplace equation is well-posed provided the data belong to a suitable function space. Explicit numerical procedures are described for approximating the solutions to these problems.
KeywordsCauchy Problem Entire Function Laplace Equation Pseudodifferential Operator Trigonometric Polynomial
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- 1.Tikhonov, A.N., Arsenin, V.Y.: Solutions of ill-posed problems. Winston-Wiley, Washington, 1977.Google Scholar
- 2.Lavrentev, M.M., Romanov, V.G., Shishatskii, S.P.: Ill-posed problems in mathematical physics and analysis. Transl. of Math. Monographs, Vol. 64, AMS, Providence, Rhode Island, 1986.Google Scholar
- 5.Tran Due Van: On the pseudo differential operators with real analytic symbols and their applications. J. Fac. Sci. Univ. Tokyo, IA Mathematics, 36, 3 (1989), 803–825.Google Scholar
- 7.Dubinskii, Yu.A.: Sobolev spaces of infinite order and differential equations. Teubner-Texte zur Mathematik, Bd. 87, Leipzig, 1986.Google Scholar
- 9.Trinh Ngoc Minh, Tran Due Van: Cauchy problems for systems of partial differential equations with a distinguished variable. Soviet Math. Dokl. 32, 2 (1985), 562–565.Google Scholar
- 10.Tran Due Van, Dinh Nho Hao, Trinh Ngoc Minh, Gorenflo, R.: On the Cauchy problems for systems of partial differential equations with a distinguished variable. To appear in J. “Numerical Functional Analysis and Optimization.”Google Scholar