Gellerstedt problem for the Lavrent’ev-Bitsadze equation in a 3D-domain. (English) Zbl 1293.35178
Summary: The spectral methods of solving boundary value problems for mixed-type differential equations of the second order in a 3D-domain are studied. Existence of a solution of the Lavrent’ev-Bitsadze problem is proved.
MSC:
| 35M12 | Boundary value problems for PDEs of mixed type |
| 35P10 | Completeness of eigenfunctions and eigenfunction expansions in context of PDEs |
| 35C10 | Series solutions to PDEs |
| 33C10 | Bessel and Airy functions, cylinder functions, \({}_0F_1\) |
Keywords:
Riesz basis; modified Bessel functions; regular solution; uniform convergence; spectral methodsReferences:
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| [6] | DOI: 10.1080/10652469.2011.632228 · Zbl 1257.35134 · doi:10.1080/10652469.2011.632228 |
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| [10] | DOI: 10.1080/10652469.2012.720255 · Zbl 1273.35191 · doi:10.1080/10652469.2012.720255 |
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