Geodesic
Explicit solution for Lamé and other PDE systems
Applications of Mathematics, Tome 51 (2006) no. 6, pp. 583-595

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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.
DOI : 10.1007/s10492-006-0022-x
Classification : 32A99, 34A05, 35C10, 35E20
Keywords: systems of linear partial differential equations; constant coefficient; explicit solutions; several complex variables; elasticity 
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     author = {Rodionov, Alexei},
     title = {Explicit solution for {Lam\'e} and other {PDE} systems},
     journal = {Applications of Mathematics},
     pages = {583--595},
     publisher = {mathdoc},
     volume = {51},
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     year = {2006},
     doi = {10.1007/s10492-006-0022-x},
     mrnumber = {2291783},
     zbl = {1164.35332},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-006-0022-x/}
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Rodionov, Alexei. Explicit solution for Lamé and other PDE systems. Applications of Mathematics, Tome 51 (2006) no. 6, pp. 583-595. doi: 10.1007/s10492-006-0022-x

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