One application of Floquet's theory toLp-Lq estimates for hyperbolic equations with very fast oscillations

DOI<link itemprop=identifier href="https://doi.org/10.1002/(SICI)1099-1476(19990725)22:11<937::AID-MMA28>3.0.CO;2-O" /><937::AID-MMA28>3.0.CO;2-O 10.1002/(SICI)1099-1476(19990725)22:11<937::AID-MMA28>3.0.CO;2-OzbMath0949.35024OpenAlexW2031736431MaRDI QIDQ4265878

Karen Yagdjian, Michael Reissig

Publication date: 1 May 2000

Full work available at URL: https://doi.org/10.1002/(sici)1099-1476(19990725)22:11<937::aid-mma28>3.0.co;2-o

zbMATH Keywords

influence of oscillations

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15) Second-order hyperbolic equations (35L10)

Related Items (15)

\(L^p-L^q\) estimates for wave equations with strong time-dependent oscillations ⋮ Small data wave maps in cyclic spacetime ⋮ Generalized energy conservation for Klein-Gordon type equations ⋮ \(C^m\)-theory of damped wave equations with stabilisation ⋮ Energy bounds for Klein-Gordon equations with time-dependent potential ⋮ Energy decay for a degenerate hyperbolic equation with a dissipative term ⋮ Lp - Lq Decay Estimates for Wave Equations with Time-Dependent Coefficients ⋮ Counter-examples of regularity behavior for \(\sigma \)-evolution equations ⋮ Global Strichartz estimates for the wave equation with time-periodic potentials ⋮ Parameteric resonance and nonexistence of the global solution to nonlinear wave equations ⋮ Construction of Parametrix to Strictly Hyperbolic Cauchy Problems with Fast Oscillations in NonLipschitz Coefficients† ⋮ \(\nu \)-loss of derivatives for an evolution type model ⋮ L p − L q Decay Estimates for the Wave Equations with Exponentially Growing Speed of Propagation ⋮ Generalised energy conservation law for wave equations with variable propagation speed ⋮ \(L_p-L_q\) decay estimates for hyperbolic equations with oscillations in coefficients

Cites Work

• Unnamed Item
• An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\)
• \(L^p\)-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I
• On \(L_2-L_{p'}\) estimates for the wave-equation
• A priori estimates for higher order hyperbolic equations
• A priori estimates for the wave equation and some applications
• Global existence for nonlinear wave equations

This page was built for publication: One application of Floquet's theory toLp-Lq estimates for hyperbolic equations with very fast oscillations