Solvability conditions of the Cauchy problem for pseudohyperbolic equations

DOI10.1134/S0037446615060075zbMath1336.35250MaRDI QIDQ259829

Gennadii V. Demidenko

Publication date: 18 March 2016

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

energy estimateSobolev spaces with exponential weightSobolev-type equation

Mathematics Subject Classification ID

Initial value problems for second-order hyperbolic equations (35L15) Pseudohyperbolic equations (35L82)

Related Items (15)

On some class of the pseudohyperbolicequations with an unknown coefficient ⋮ Blow-up and global solvability of the Cauchy problem for a pseudohyperbolic equation related to the generalized Boussinesq equation ⋮ On well-posedness of the Cauchy problem for pseudohyperbolic equations in weighted Sobolev spaces ⋮ Solution blow-up and global solvability of the Cauchy problem for the equation of moderately long longitudinal waves in a viscoelastic rod ⋮ Boundary value problems for the Rayleigh-Bishop equation in a quarter plane ⋮ BOUNDARY VALUE PROBLEM IN A CYLINDER FOR A PSEUDOHYPERBOLIC EQUATION ⋮ Blow-up of the solution to the equation for nonlinear beam vibrations with allowance for transverse deformation effects ⋮ Upon the concept of index of linear partial differential-algebraic equations ⋮ Cauchy problem for one pseudohyperbolic system ⋮ Cauchy problem for the equation of torsional vibrations of a rod in a viscoelastic medium ⋮ The Cauchy problem for the nonlinear long longitudinal waves equation in a viscoelastic rod ⋮ Cauchy problem for the torsional vibration equation of a nonlinear-elastic rod of infinite length ⋮ Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition ⋮ On solvability of the boundary value problem for one pseudohyperbolic equation ⋮ Solvability of the Cauchy problem for a pseudohyperbolic system

Cites Work

• The Cauchy problem for hyperbolic equations not resolved with respect to the highest time derivative
• On solvability of the Cauchy problem for pseudohyperbolic equations
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