On a local existence theorem of Neumann problem for some quasilinear hyperbolic system of 2nd order

DOI10.1007/BF01180683zbMath0652.35077OpenAlexW2066823523MaRDI QIDQ1107036

Yoshihiro Shibata, Gen Nakamura

Publication date: 1989

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174075

zbMATH Keywords

local existencequasilinearclassical solutionshyperbolic-elliptic systemNeumann type boundary conditionfully nonlinear boundary conditionelastodynamical systemsnonlinear acoustical equations

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Second-order nonlinear hyperbolic equations (35L70)

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Cites Work

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• Lectures on three-dimensional elasticity. Notes by S. Kesavan
• Energy methods for quasilinear hyperbolic initial-boundary value problems. Applications to elastodynamics
• On the positivity of the second variation in finite elasticity
• On the Neumann problem for some linear hyperbolic systems of second order
• Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity
• On Besov spaces and Sobolev spaces of generalized functions defined on a general region
• A mixed problem for hyperbolic equations of second order with non- homogeneous Neumann type boundary condition
• Sur les problèmes de Cauchy hyperboliques bien posés
• Local existence of solution for the initial boundary value problem of fully nonlinear wave equation
• On a Global Existence Theorem of Neumann Problem for Some Quasi-Linear Hyperbolic Equations
• Das Rand-Anfangswertproblem für quasilineare Wellengleichungen in Sobolevräumen niedriger Ordnung.
• Delayed singularity formation in solution of nonlinear wave equations in higher dimensions
• Finite amplitude waves in a homogeneous isotropic elastic solid

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