scientific article
From MaRDI portal
Publication:3207471
zbMath0417.35049MaRDI QIDQ3207471
Ferruccio Colombini, Ennio De Giorgi, Sergio Spagnolo
Publication date: 1979
Full work available at URL: http://www.numdam.org/item?id=ASNSP_1979_4_6_3_511_0
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
perturbationa priori estimatesGevrey classexistence and uniquenesshyperbolic equationanalytic solutionscoercive equations
A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15) Second-order hyperbolic equations (35L10)
Related Items
A Few Remarks on Hyperbolic Systems with Zygmund in Time Coefficients ⋮ Unnamed Item ⋮ Optimal derivative loss for abstract wave equations ⋮ On the wave equation with space dependent coefficients: singularities and lower order terms ⋮ Subelliptic Gevrey spaces ⋮ Response solutions for wave equations with variable wave speed and periodic forcing ⋮ On the Cauchy problem for microlocally symmetrizable hyperbolic systems with log-Lipschitz coefficients ⋮ Three examples of residual pathologies ⋮ Some local questions for hyperbolic systems with non-regular time dependent coefficients ⋮ Modulus of Continuity and Decay at Infinity in Evolution Equations with Real Characteristics ⋮ Energy inequality for non strictly hyperbolic operators in the Gevrey class ⋮ Unnamed Item ⋮ The Cauchy problem for 𝑝-evolution equations ⋮ Degenerate Kirchhoff equation in ultradifferentiable class ⋮ Unnamed Item ⋮ On the wave equation with multiplicities and space-dependent irregular coefficients ⋮ Unnamed Item ⋮ Modulus of continuity of the coefficients and loss of derivatives in the strictly hyperbolic Cauchy problem ⋮ Quasilinear hyperbolic operators with log-Lipschitz coefficients ⋮ Operators of \(p\)-evolution with nonregular coefficients in the time variable ⋮ Weakly hyperbolic systems with Hölder continuous coefficients ⋮ Un résultat sur les fonctions de classe \(C^{1,\alpha}\) et application au problème de Cauchy. (A result for functions of class \(C^{1,\alpha}\) and application to the Cauchy problem) ⋮ Hyperbolic equations and classes of infinitely differentiable functions ⋮ On a quasilinear wave equation with memory ⋮ Hyperbolic systems with non-diagonalisable principal part and variable multiplicities. I: Well-posedness ⋮ Modulus of continuity of the coefficients and (non)quasianalytic solutions in the strictly hyperbolic Cauchy problem ⋮ A note on a theorem of Jörgens ⋮ A uniqueness result for Kirchhoff equations with non-Lipschitz nonlinear term ⋮ Hyperbolic operators with non-Lipschitz ceofficients ⋮ On second order hyperbolic equations with coefficients degenerating at infinity and the loss of derivatives and decays ⋮ A generalized internal control for the wave equation in a rectangle ⋮ Energy estimates at infinity for hyperbolic equations with oscillating coefficients ⋮ Log-Lipschitz regularity for SG hyperbolic systems ⋮ The log-effect for \(2\) by \(2\) hyperbolic systems ⋮ Some results of Gevrey and analytic regularity for semilinear weakly hyperbolic equations of Oleinik type ⋮ Unnamed Item ⋮ Long time existence for the bosonic membrane in the light cone gauge ⋮ Some examples of hyperbolic equations without local solvability ⋮ Deterministic and stochastic Cauchy problems for a class of weakly hyperbolic operators on \(\mathbb{R}^n\) ⋮ No loss of derivatives for hyperbolic operators with Zygmund-continuous coefficients in time ⋮ Well-posedness of hyperbolic systems with multiplicities and smooth coefficients ⋮ Analytic regularity for a class of semi-linear weakly hyperbolic equations of second order ⋮ On a weakly hyperbolic equation with a term of order zero ⋮ Weakly hyperbolic equations with non-analytic coefficients and lower order terms ⋮ Inhomogeneous wave equation with \(t\)-dependent singular coefficients ⋮ A well-posedness result for hyperbolic operators with Zygmund coefficients ⋮ Well-posedness of low regularity solutions to the second order strictly hyperbolic equations with non-Lipschitzian coefficients ⋮ On the global controllability of the \(1\)-D Boussinesq equation ⋮ The Cauchy problem for Kirchhoff equations ⋮ Wave equation for operators with discrete spectrum and irregular propagation speed ⋮ Linear wave equations with time-dependent propagation speed and strong damping ⋮ A generalized Levi condition for weakly hyperbolic Cauchy problems with coefficients low regular in time and smooth in space ⋮ On some hyperbolic equations of third order ⋮ On weakly hyperbolic operators with non-regular coefficients and finite order degeneration. ⋮ Hölder continuity in time for SG hyperbolic systems ⋮ Cauchy problems for hyperbolic systems in \(\mathbb{R}^n\) with irregular principal symbol in time and for \(x \rightarrow \infty \) ⋮ Gevrey-well-posedness for weakly hyperbolic operators with non-regular coefficients. ⋮ On the optimal regularity of coefficients in hyperbolic Cauchy problems. ⋮ Time regularity of the solutions to second order hyperbolic equations ⋮ Generalised hyperbolicity in spacetimes with Lipschitz regularity ⋮ On second order weakly hyperbolic equations and the ultradifferentiable classes ⋮ On the well-posedness of weakly hyperbolic equations with time-dependent coefficients ⋮ Asymptotic behaviour as \(t \to +\infty\) of the solutions of linear hyp equations with coefficients discontinuous in time (on a bounded domain) ⋮ First order linear partial differential equations with discontinuous coefficients ⋮ Second order hyperbolic equations with coefficients real analytic in space variables and discontinuous in time ⋮ Embeddings and characterizations of Lipschitz spaces ⋮ Gevrey well-posedness of an abstract Cauchy problem of weakly hyperbolic type ⋮ On the Cauchy problem for finitely degenerate hyperbolic equations of second order ⋮ Finite vs infinite derivative loss for abstract wave equations with singular time-dependent propagation speed ⋮ Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters ⋮ Strictly Hyperbolic Cauchy Problems with Coefficients Low-Regular in Time and Space ⋮ Quasianalytic and nonquasianalytic solutions for a class of weakly hyperbolic Cauchy problems ⋮ On the asymptotic behavior of the energy for the wave equations with time depending coefficients ⋮ Third order homogeneous weakly hyperbolic equations with nonanalytic coefficients ⋮ On the energy estimates of the wave equation with time dependent propagation speed asymptotically monotone functions ⋮ Well posedness under Levi conditions for a degenerate second order Cauchy problem ⋮ On hyperbolic equations and systems with non-regular time dependent coefficients ⋮ Global in time solutions of evolution equations in scales of Banach function spaces in \(\mathbb R^n\) ⋮ A degenerate hyperbolic equation under Levi conditions ⋮ Loss of derivatives in evolution Cauchy problems ⋮ A dyadic decomposition approach to a finitely degenerate hyperbolic problem ⋮ Kirchhoff equations with strong damping ⋮ On hyperbolic systems with time-dependent Hölder characteristics ⋮ Time-dependent propagation speed vs strong damping for degenerate linear hyperbolic equations ⋮ Propagation of singularities in the Cauchy problem for a class of degenerate hyperbolic operators ⋮ Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field ⋮ On the energy estimates of semi-discrete wave equations with time dependent propagation speed ⋮ Critical counterexamples for linear wave equations with time-dependent propagation speed ⋮ Backward uniqueness for parabolic operators whose coefficients are non-Lipschitz continuous in time ⋮ A note on weakly hyperbolic equations with analytic principal part ⋮ Unnamed Item ⋮ Strictly hyperbolic equations with coefficients low-regular in time and smooth in space ⋮ Very weak solutions to hypoelliptic wave equations ⋮ Time-dependent wave equations on graded groups ⋮ Space regularity for evolution operators modeled on Hörmander vector fields with time dependent measurable coefficients ⋮ The Cauchy problem for a class of Kovalevskian pseudo-differential operators ⋮ Asymptotically free property of the solutions of an abstract linear hyperbolic equation with time-dependent coefficients ⋮ Lifespan of solutions to semilinear damping wave equations in De Sitter spacetime ⋮ Spectral gap global solutions for degenerate Kirchhoff equations ⋮ On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in \(t\) and degenerate in \(t=T\) ⋮ Discrete time-dependent wave equations. I. Semiclassical analysis ⋮ An example of a weakly hyperbolic Cauchy problem not well posed in \(C^\infty\) ⋮ Energy estimate and fundamental solution for degenerate hyperbolic Cauchy problems ⋮ Abstract linear hyperbolic equations with variable domain ⋮ Linear second order differential equations in Hilbert spaces. The Cauchy problem and asymptotic behaviour for large time ⋮ A new result on backward uniqueness for parabolic operators ⋮ Wave equation for sums of squares on compact Lie groups ⋮ On the propagation of the analytic regularity in strictly hyperbolic equations which are lipschitz continuous with respect to time ⋮ Fourier integral operators in Gevrey class on \({\mathbb{R}}^ n\) and the fundamental solution for a hyperbolic operator ⋮ Hyperbolic second order equations with non-regular time dependent coefficients ⋮ Hyperbolic equations with cofficients rapidly oscillating in time: a result of nonstability ⋮ Weak observability estimates for 1-D wave equations with rough coefficients ⋮ Regularly hyperbolic systems and Gevrey classes ⋮ On the Gevrey well posedness of the Cauchy problem for weakly hyperbolic equations of higher order ⋮ Hyperbolic equations with coefficients rapidly oscillating in time: A result of nonstability ⋮ Well-posedness for hyperbolic equations whose coefficients lose regularity at one point ⋮ On backward uniqueness for parabolic equations when Osgood continuity of the coefficients fails at one point
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Sur les fonctionnelles analytiques et la transformation de Fourier-Borel
- Ultra-distributions definies sur \(R^ n\) et sur certaines classes de variétés différentiables
- Sur quelques extensions de la notion de distribution
- On the convergence of solutions of hyperbolic equations
- Questions of Existence and Uniqueness for Hyperbolic Equations with Discontinuous Coefficients