Displaying similar documents to “On a linear hyperbolic equation with smooth coefficients without solutions”

Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

Enrico Bernardi, Antonio Bove, Vesselin Petkov (2010)

Journées Équations aux dérivées partielles

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We study a class of third order hyperbolic operators P in G = Ω ∩ { 0 ≤ t ≤ T } , Ω ⊂ ℝ n + 1 with triple characteristics on t = 0 . We consider the case when the fundamental matrix of the principal symbol for t = 0 has a couple of non vanishing real eigenvalues and P is strictly hyperbolic for t > 0 . We prove that P is strongly hyperbolic, that is the Cauchy problem for P + Q is well posed in G for any lower order terms Q .

L p - L q -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki (1991)

Annales Polonici Mathematici

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We prove the L p - L q -time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the L p - L q -time decay estimates.

On the well posedness of vanishing viscosity limits

Alberto Bressan (2002)

Journées équations aux dérivées partielles

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This paper provides a survey of recent results concerning the stability and convergence of viscous approximations, for a strictly hyperbolic system of conservation laws in one space dimension. In the case of initial data with small total variation, the vanishing viscosity limit is well defined. It yields the unique entropy weak solution to the corresponding hyperbolic system.

Dunkl hyperbolic equations.

Mejjaoli, Hatem (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On some variational inequalities for nonclassical type operators

Sergey Glazatov (1992)

Banach Center Publications

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The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.