Explicit solution for Lamé and other PDE systems

Alexei Rodionov

Applications of Mathematics (2006)

  • Volume: 51, Issue: 6, page 583-595
  • ISSN: 0862-7940

Abstract

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We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.

How to cite

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Rodionov, Alexei. "Explicit solution for Lamé and other PDE systems." Applications of Mathematics 51.6 (2006): 583-595. <http://eudml.org/doc/33268>.

@article{Rodionov2006,
abstract = {We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.},
author = {Rodionov, Alexei},
journal = {Applications of Mathematics},
keywords = {systems of linear partial differential equations; constant coefficient; explicit solutions; several complex variables; elasticity; systems of linear partial differential equations; constant coefficient},
language = {eng},
number = {6},
pages = {583-595},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Explicit solution for Lamé and other PDE systems},
url = {http://eudml.org/doc/33268},
volume = {51},
year = {2006},
}

TY - JOUR
AU - Rodionov, Alexei
TI - Explicit solution for Lamé and other PDE systems
JO - Applications of Mathematics
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 51
IS - 6
SP - 583
EP - 595
AB - We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The equations of three dimensional elastic equilibrium are solved as an example. Another convergence theorem is proved for this particular system. We also consider a possibility to represent solutions in a finite form as partial sums of the series with terms depending on several complex variables.
LA - eng
KW - systems of linear partial differential equations; constant coefficient; explicit solutions; several complex variables; elasticity; systems of linear partial differential equations; constant coefficient
UR - http://eudml.org/doc/33268
ER -

References

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  1. 10.1016/S0893-9659(00)00030-6, Appl. Math. Lett. 13 (2000), 33–39. (2000) Zbl0973.35049MR1760260DOI10.1016/S0893-9659(00)00030-6
  2. Polynomial solutions to systems of partial differential equations with constant coefficients, Yokohama Math.  J. 47 (2000), 121–142. (2000) Zbl0971.35014MR1763777
  3. 10.1006/aima.1996.0005, Adv. Math. 117 (1996), 157–163. (1996) MR1367588DOI10.1006/aima.1996.0005
  4. 10.1016/0010-4655(95)00083-R, Comput. Phys. Commun. 90 (1995), 102–116. (1995) DOI10.1016/0010-4655(95)00083-R
  5. Applying the theory of functions of two complex variables to the theory of elasticity, Sov. Phys., Dokl. 22 (1977), 48–50. (1977) Zbl0375.73018

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