Well posedness in the C∞ class for utt=a(u)Δu

DOI10.1016/S0362-546X(97)00703-7zbMath0919.35004MaRDI QIDQ4238419

Renato Manfrin

Publication date: 2 September 1999

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

quasi-linear wave equationweakly hyperbolic

Mathematics Subject Classification ID

Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items

Local well-posedness for a quasilinear Schroedinger equation with degenerate dispersion, Finite-time degeneration of hyperbolicity without blowup for quasilinear wave equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A necessary and sufficient condition for the hyperbolicity of second order equations with two independent variables
• Gevrey well-posedness of an abstract Cauchy problem of weakly hyperbolic type
• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• The Cauchy problem for hyperbolic equations with double characteristics
• Non-uniqueness in hyperbolic Cauchy problems
• The Cauchy problem for quasi-linear symmetric hyperbolic systems
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• Global existence for abstract evolution equations of weakly hyperbolic type
• A solvability result for a nonlinear weakly hyperbolic equation of second order
• Équations et systèmes non-linéaires, hyperboliques non-stricts
• Hyperbolic systems of conservation laws II
• The cauchy problem for weakly hyperbolic equation
• The cauchy problem for weakly hyperbolic equations of second order
• Local solvability in c^∞for quasi-linear weakly hyperbolic equations of second order