Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions

Małgorzata Zdanowicz; Zbigniew Peradzyński

The search session has expired. Please query the service again.

Displaying similar documents to “Propagation of weak discontinuities for quasilinear hyperbolic systems with coefficients functionally dependent on solutions”

Semilinear hyperbolic functional equations

László Simon (2014)

Banach Center Publications

Similarity:

We consider second order semilinear hyperbolic functional differential equations where the lower order terms contain functional dependence on the unknown function. Existence and uniqueness of solutions for t ∈ (0,T), existence for t ∈ (0,∞) and some qualitative properties of the solutions in (0,∞) are shown.

On the existence and uniqueness of solutions of the Goursat problem for systems of functional partial differential equations of hyperbolic type.

Grigolia, M. (1999)

Memoirs on Differential Equations and Mathematical Physics

Similarity:

Generalized Cauchy problems for hyperbolic functional differential systems

Elżbieta Puźniakowska-Gałuch (2014)

Annales Polonici Mathematici

Similarity:

A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.

Existence of global weak solutions for a class of quasilinear hyperbolic integro-differential equations describing visco-elastic materials.

Hamid Bellout, Jindrich Necas (1994)

Mathematische Annalen

Similarity:

On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables

Tomasz Człapiński (1997)

Annales Polonici Mathematici

Similarity:

We seek for classical solutions to hyperbolic nonlinear partial differential-functional equations of the second order. We give two theorems on existence and uniqueness for problems with nonlocal conditions in bounded and unbounded domains.

Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form

Jan Turo (1989)

Annales Polonici Mathematici

Similarity:

The weak basis theorem

Charles McArthur (1967)

Colloquium Mathematicae

Similarity:

A boundary value problem for quasilinear hyperbolic systems with a retarded argument

Z. Kamont, J. Turo (1987)

Annales Polonici Mathematici

Similarity:

On the stabiltiy of a system of functional equations characterizing generalize hyperbolic and trigonometric functions.

Jens Schwaiger, Wolfgang Förg-Rob (1993)

Aequationes mathematicae

Similarity:

On the local Cauchy problem for nonlinear hyperbolic functional differential equations

Tomasz Człapiński (1997)

Annales Polonici Mathematici

Similarity:

We consider the local initial value problem for the hyperbolic partial functional differential equation of the first order (1) $D ₓ z (x, y) = f (x, y, z (x, y), (W z) (x, y), D_{y} z (x, y))$ on E, (2) z(x,y) = ϕ(x,y) on [-τ₀,0]×[-b,b], where E is the Haar pyramid and τ₀ ∈ ℝ₊, b = (b₁,...,bₙ) ∈ ℝⁿ₊. Using the method of bicharacteristics and the method of successive approximations for a certain functional integral system we prove, under suitable assumptions, a theorem on the local existence of weak solutions of the problem (1),(2).