Displaying similar documents to “Hyperbolic differential-operator equations on a whole axis.”

Some non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type

A. Berdyshev, E. Karimov (2006)

Open Mathematics

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In this work two non-local problems for the parabolic-hyperbolic type equation with non-characteristic line of changing type are considered. Unique solvability of these problems is proven. The uniqueness of the solution is proven by the method of energy integrals and the existence is proven by the method of integral equations.

Linear hyperbolic problems in the whole scale of Sobolev-type spaces of periodic functions

Irina Kmit (2007)

Commentationes Mathematicae Universitatis Carolinae

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We study one-dimensional linear hyperbolic systems with L ∞ -coefficients subjected to periodic conditions in time and reflection boundary conditions in space. We derive a priori estimates and give an operator representation of solutions in the whole scale of Sobolev-type spaces of periodic functions. These spaces give an optimal regularity trade-off for our problem.