Some partial differential equations in Clifford analysis

Elena Obolashvili

Banach Center Publications (1996)

  • Volume: 37, Issue: 1, page 173-179
  • ISSN: 0137-6934

Abstract

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Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.

How to cite

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Obolashvili, Elena. "Some partial differential equations in Clifford analysis." Banach Center Publications 37.1 (1996): 173-179. <http://eudml.org/doc/208594>.

@article{Obolashvili1996,
abstract = {Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.},
author = {Obolashvili, Elena},
journal = {Banach Center Publications},
keywords = {boundary and initial value problems},
language = {eng},
number = {1},
pages = {173-179},
title = {Some partial differential equations in Clifford analysis},
url = {http://eudml.org/doc/208594},
volume = {37},
year = {1996},
}

TY - JOUR
AU - Obolashvili, Elena
TI - Some partial differential equations in Clifford analysis
JO - Banach Center Publications
PY - 1996
VL - 37
IS - 1
SP - 173
EP - 179
AB - Using Clifford analysis in a multidimensional space some elliptic, hyperbolic and parabolic systems of partial differential equations are constructed, which are related to the well-known classical equations. To obtain parabolic systems Clifford algebra is modified and some corresponding differential operator is constructed. For systems obtained the boundary and initial value problems are solved.
LA - eng
KW - boundary and initial value problems
UR - http://eudml.org/doc/208594
ER -

References

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  1. [1] M. Begher, R. Gilbert, Piecewise continuous solution of pseudoparabolic equations in two space dimensions, Proc. Royal Soc. Edinburgh 81A (1978), 153-173. Zbl0395.35047
  2. [2] A. Bitsadze, Boundary value problems of elliptic equations of second order, Nauka, Moscow, 1966 (Russian). Zbl0167.09401
  3. [3] F. Brack, R. Delanghe, F. Sommen, Clifford Analysis, Pitman, London, 1982. 
  4. [4] A. Dzhuraev, On the Moisil-Theodorescu system, P.D.E. with complex analysis, (editors H. Begher and A. Jeffrey), Longman Scient. and Techn. 1992, 186-203. Zbl0826.35017
  5. [5] K. Gurlebeck, W. Sproßig, Quaternionic analysis and elliptic boundary value problems, Akademie-Verlag, Berlin 1989. Zbl0699.35007
  6. [6] K. Habetha, Function theory in algebras. Complex analysis, Methods, Trends and Applications. Ak. Verlag, Berlin 1983, 225-237. 
  7. [7] V. Iftime, Fonctions hypercomplexes. Bull. Math. R. S. de Roumanie 9(57) (1965), 279-332. 
  8. [8] H. Liede, The existence and uniqueness theorems of the linear and nonlinear R.-H. problems for the generalized holomorphic vector of the second kind, Acta Math. Sci. Engl. Ed. 10 no. 2 (1990), 185-199. Zbl0722.30025
  9. [9] G. Moisil, N. Theodorescu, Fonctions holomorphes dans l'espace, Mathematica 5 (1931). 
  10. [10a] E. Obolashvili, Space generalized holomorphic vectors, Diff. Urav. T.XI.1, 1975, 108-115. Minsk (Russian). 
  11. [10b] E. Obolashvili, Effective solutions of some boundary value problems in two and three dimensional cases, Functional analytic methods in complex analysis and applications to PDE, 1988.Trieste, 149-172. 
  12. [10c] E. Obolashvili, Some boundary value problems for metaparabolic equations (Russian). Proceeding of I. Vekua Inst. of Applied math. T.1, N.1, 1985, 161-164. 

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