Displaying similar documents to “On some boundary value problems for a class of hyperbolic systems of second order in conic domains.”

Existence and non-existence of global solutions for nonlinear hyperbolic equations of higher order

Guo Wang Chen, Shu Bin Wang (1995)

Commentationes Mathematicae Universitatis Carolinae

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The existence and uniqueness of classical global solution and blow up of non-global solution to the first boundary value problem and the second boundary value problem for the equation u t t - α u x x - β u x x t t = ϕ ( u x ) x are proved. Finally, the results of the above problem are applied to the equation arising from nonlinear waves in elastic rods u t t - a 0 + n a 1 ( u x ) n - 1 u x x - a 2 u x x t t = 0 .

On the mixed problem for hyperbolic partial differential-functional equations of the first order

Tomasz Człapiński (1999)

Czechoslovak Mathematical Journal

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We consider the mixed problem for the hyperbolic partial differential-functional equation of the first order D x z ( x , y ) = f ( x , y , z ( x , y ) , D y z ( x , y ) ) , where z ( x , y ) [ - τ , 0 ] × [ 0 , h ] → ℝ is a function defined by z ( x , y ) ( t , s ) = z ( x + t , y + s ) , ( t , s ) ∈ [ - τ , 0 ] × [ 0 , h ] . Using the method of bicharacteristics and the method of successive approximations for a certain integral-functional system we prove, under suitable assumptions, a theorem of the local existence of generalized solutions of this problem.

On local motion of a compressible barotropic viscous fluid bounded by a free surface

W. Zajączkowski (1992)

Banach Center Publications

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We consider the motion of a viscous compressible barotropic fluid in ℝ³ bounded by a free surface which is under constant exterior pressure, both with surface tension and without it. In the first case we prove local existence of solutions in anisotropic Hilbert spaces with noninteger derivatives. In the case without surface tension the anisotropic Sobolev spaces with integration exponent p > 3 are used to omit the coefficients which are increasing functions of 1/T, where T is the...