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  • Cited by 6
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Mantzavinos, D. Papadomanolaki, M.G. Saridakis, Y.G. and Sifalakis, A.G. 2016. Fokas transform method for a brain tumor invasion model with heterogeneous diffusion in 1+1 dimensions. Applied Numerical Mathematics, Vol. 104, p. 47.

    Sheils, N E and Smith, D A 2015. Heat equation on a network using the Fokas method. Journal of Physics A: Mathematical and Theoretical, Vol. 48, Issue. 33, p. 335001.

    Fokas, A S and De Lillo, S 2014. The unified transform for linear, linearizable and integrable nonlinear partial differential equations. Physica Scripta, Vol. 89, Issue. 3, p. 038004.

    Fokas, A. S. and Kalimeris, K. 2014. Eigenvalues for the Laplace Operator in the Interior of an Equilateral Triangle. Computational Methods and Function Theory, Vol. 14, Issue. 1, p. 1.

    MANTZAVINOS, DIONYSSIOS and FOKAS, ATHANASSIOS S. 2013. The unified method for the heat equation: I. non-separable boundary conditions and non-local constraints in one dimension. European Journal of Applied Mathematics, Vol. 24, Issue. 06, p. 857.

    Pelloni, B. and Smith, D. A. 2013. Spectral theory of some non-selfadjoint linear differential operators. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 469, Issue. 2154, p. 20130019.

  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 152, Issue 3
  • May 2012, pp. 473-496

Well-posed two-point initial-boundary value problems with arbitrary boundary conditions

  • DAVID A. SMITH (a1)
  • DOI:
  • Published online: 12 December 2011

We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed problems using Fokas' transform method. We also give a sufficient condition guaranteeing that the solution can be represented using a series.

The relevant condition, the analyticity at infinity of certain meromorphic functions within particular sectors, is significantly more concrete and easier to test than the previous criterion, based on the existence of admissible functions.

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[4]A. S. Fokas . Two dimensional linear partial differential equations in a convex polygon. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 457 (2001), 371393.

[6]A. S. Fokas and B. Pelloni . Method for solving moving boundary value problems for linear evolution equations. Phys. Rev. Lett. 84 (2000), no. 21, 47854789.

[8]A. S. Fokas and B. Pelloni . A transform method for linear evolution PDEs on a finite interval. IMA J. Appl. Math. 70 (2005), 564587.

[11]E. Langer . The zeros of exponential sums and integrals. Bull. Amer. Math. Soc. 37 (1931), 213239.

[13]B. Pelloni . The spectral representation of two-point boundary-value problems for third-order linear evolution partial differential equations. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2005), 29652984.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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