Singularities of Solutions to Cauchy Problems for Semilinear Wave Equations in Two Space Dimensions

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Volume 3, Issue 1

Yu Yuenian

J. Part. Diff. Eq.,3(1990),pp.69-80

Published online: 1990-03

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Abstract

This paper concerns the Cauchy problem for semilinear wave equations with two space variables, of which the initial data have conormal singularities on finite curves intersecting at one point on the initial plane. It is proved that the solution is of conormal distribution type, and its singularities are contained in the union of the characteristic surfaces through these curves and the characteristic cone issuing from the intersection point.

Keywords

Semilinear wave equations propagation of singulatities conormat distributions

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@Article{JPDE-3-69, author = {Yu Yuenian}, title = {Singularities of Solutions to Cauchy Problems for Semilinear Wave Equations in Two Space Dimensions}, journal = {Journal of Partial Differential Equations}, year = {1990}, volume = {3}, number = {1}, pages = {69--80}, abstract = { This paper concerns the Cauchy problem for semilinear wave equations with two space variables, of which the initial data have conormal singularities on finite curves intersecting at one point on the initial plane. It is proved that the solution is of conormal distribution type, and its singularities are contained in the union of the characteristic surfaces through these curves and the characteristic cone issuing from the intersection point.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5791.html} }

TY - JOUR T1 - Singularities of Solutions to Cauchy Problems for Semilinear Wave Equations in Two Space Dimensions AU - Yu Yuenian JO - Journal of Partial Differential Equations VL - 1 SP - 69 EP - 80 PY - 1990 DA - 1990/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5791.html KW - Semilinear wave equations KW - propagation of singulatities KW - conormat distributions AB - This paper concerns the Cauchy problem for semilinear wave equations with two space variables, of which the initial data have conormal singularities on finite curves intersecting at one point on the initial plane. It is proved that the solution is of conormal distribution type, and its singularities are contained in the union of the characteristic surfaces through these curves and the characteristic cone issuing from the intersection point.

Yu Yuenian. (1990). Singularities of Solutions to Cauchy Problems for Semilinear Wave Equations in Two Space Dimensions. Journal of Partial Differential Equations. 3 (1). 69-80. doi:

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