A canonical form of a system of microdifferential equations with non- involutory characteristics and branching of singularities

DOI10.1007/BF01396633zbMath0493.35083MaRDI QIDQ5966542

Toshinori Oaku

Publication date: 1982

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142864

zbMATH Keywords

regular singularitiesmicrodifferential equationsregular involutory submanifolds

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Shocks and singularities for hyperbolic equations (35L67) Propagation of singularities; initial value problems on manifolds (58J47)

Related Items (10)

Singular cauchy problems for a class of weakly hyperbolic differential operators ⋮ A hyperbolic approach to elliptic and parabolic singular perturbation problems ⋮ Uniqueness in the characteristic Cauchy problem under a convexity condition ⋮ Microdifferential equations with non-involutory characteristics ⋮ Propogation Des Singularites pour Des Operateurs dont La Matrice Foundament contient Des Valeurs propres non Purement Imaginaires ⋮ Propagation of singularities in the ramified Cauchy problem for a class of operators with non-involutive multiple characteristics ⋮ Exact propagators for some degenerate hyperbolic operators ⋮ Exact solutions and branching of singularities for some hyperbolic equations in two variables ⋮ Analytic hypo-ellipticity and propagation of regularity for a system of microdifferential equations with non-involutory characteristics ⋮ Analytic hypo-ellipticity and propagation of regularity for operators with non-involutory characteristics

Cites Work

• Branching of singularities for degenerate hyperbolic operators and Stokes phenomena
• Propagation of micro-analyticity for solutions of pseudo-differential equations. I
• Wave fronts of solutions of certain pseudodifferential equations
• Systems of differential equations with regular singularities and their boundary value problems
• Propagation at the boundary and reflection of analytic singularities of solutions of linear partial differential equations. I
• Micro-hyperbolic systems
• On holonomic systems of microdifferential equations. III: Systems with regular singularities
• Pseudo-differential operators and Gevrey classes
• Boundary values of hyperfunction solutions of linear partial differential equations
• Propagation of singularities and uniqueness in the cauchy problem at a class of doubly characteristic points
• Structure of cohomology groups whose coefficients are microfunction solution sheaves of systems of pseudo-differential equations withmultiple characteristics, I
• On the theorem of Cauchy-Kowalevsky for first order linear differential equations with degenerate principal symbols
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