Volume 1, Issue 1
Cauchy Problem for a Class of Totally Characteristic Hyperbolic Operators with Characteristics of Variable Multiplicity in Gevrey Classes

Chen Hua

J. Part. Diff. Eq.,1(1988),pp.31-41

Published online: 1988-01

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  • Abstract

This paper studies tho Cauchy problem of totally characteristic hyperbolic operator (1.1) in Gevrey classes, and obtains the following main result: Under the conditions (I) - (VI), if 1 ≤ s < \frac{σ}{σ-1} (σ is definded by (1.7)). then the Cauchy problem (1.1) is wellposed in B ([0, T], G^s_{L²}, (R^n)); if s = \frac{σ}{σ-1}, then the Cauchy problem (1.1) is wellpooed in B ([0, e], G^{\frac{σ}{σ-1}}_{L²}(R^n)) (where e > 0, small enough).

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@Article{JPDE-1-31, author = {}, title = {Cauchy Problem for a Class of Totally Characteristic Hyperbolic Operators with Characteristics of Variable Multiplicity in Gevrey Classes}, journal = {Journal of Partial Differential Equations}, year = {1988}, volume = {1}, number = {1}, pages = {31--41}, abstract = { This paper studies tho Cauchy problem of totally characteristic hyperbolic operator (1.1) in Gevrey classes, and obtains the following main result: Under the conditions (I) - (VI), if 1 ≤ s < \frac{σ}{σ-1} (σ is definded by (1.7)). then the Cauchy problem (1.1) is wellposed in B ([0, T], G^s_{L²}, (R^n)); if s = \frac{σ}{σ-1}, then the Cauchy problem (1.1) is wellpooed in B ([0, e], G^{\frac{σ}{σ-1}}_{L²}(R^n)) (where e > 0, small enough). }, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5850.html} }
TY - JOUR T1 - Cauchy Problem for a Class of Totally Characteristic Hyperbolic Operators with Characteristics of Variable Multiplicity in Gevrey Classes JO - Journal of Partial Differential Equations VL - 1 SP - 31 EP - 41 PY - 1988 DA - 1988/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5850.html KW - AB - This paper studies tho Cauchy problem of totally characteristic hyperbolic operator (1.1) in Gevrey classes, and obtains the following main result: Under the conditions (I) - (VI), if 1 ≤ s < \frac{σ}{σ-1} (σ is definded by (1.7)). then the Cauchy problem (1.1) is wellposed in B ([0, T], G^s_{L²}, (R^n)); if s = \frac{σ}{σ-1}, then the Cauchy problem (1.1) is wellpooed in B ([0, e], G^{\frac{σ}{σ-1}}_{L²}(R^n)) (where e > 0, small enough).
Chen Hua. (1970). Cauchy Problem for a Class of Totally Characteristic Hyperbolic Operators with Characteristics of Variable Multiplicity in Gevrey Classes. Journal of Partial Differential Equations. 1 (1). 31-41. doi:
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