ENERGY ESTIMATES FOR WEAKLY HYPERBOLIC SYSTEMS OF THE FIRST ORDER

DOI10.1142/S0219199705001969zbMath1097.35109arXivmath/0311027MaRDI QIDQ3379448

Ingo Witt, Michael Dreher

Publication date: 6 April 2006

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0311027

zbMATH Keywords

well-posednessloss of regularitySobolev-type spacescoefficients depending on the spatial variables

Mathematics Subject Classification ID

Initial value problems for first-order hyperbolic systems (35L45) Degenerate hyperbolic equations (35L80) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (4)

A note on initial value problem for the generalized Tricomi equation in a mixed-type domain ⋮ On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains ⋮ On the existence and cusp singularity of solutions to semilinear generalized Tricomi equations with discontinuous initial data ⋮ On a regularity result for the transonic pressure-gradient system in gas dynamics

Cites Work

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• Branching of singularities for degenerate hyperbolic operators
• Edge Sobolev spaces and weakly hyperbolic equations
• Fundamental solution for a hyperbolic system with diagonal principal part
• Parametrix of certain weakly hyperbolic operators
• Hypoelliptic operators with double characteristics and related pseudo-differential operators
• NECESSARY CONDITIONS FOR THE CAUCHY PROBLEM FOR NON-STRICTLY HYPERBOLIC EQUATIONS TO BE WELL-POSED
• A symbolic construction of the forward fundamental solution of the wave operator
• Propagation of mild singularities for semilinear weakly hyperbolic equations

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