Cauchy Problem for a Class of Totally Characteristic Hyperbolic Operators with Characteristics of Variable Multiplicity in Gevrey Classes
Year: 1988
Journal of Partial Differential Equations, Vol. 1 (1988), Iss. 1 : pp. 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).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1988-JPDE-5850
Journal of Partial Differential Equations, Vol. 1 (1988), Iss. 1 : pp. 31–41
Published online: 1988-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 11