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

Tomasz Człapiński

Displaying similar documents to “On the mixed problem for hyperbolic partial differential-functional equations of the first order”

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

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On the mixed problem for quasilinear partial functional differential equations with unbounded delay

Tomasz Człapiński (1999)

Annales Polonici Mathematici

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We consider the mixed problem for the quasilinear partial functional differential equation with unbounded delay $D_{t} z (t, x) = \sum_{i = 1}^{n} f_{i} (t, x, z_{(t, x)}) D_{x_{i}} z (t, x) + h (t, x, z_{(t, x)})$ , where $z_{(t, x)} \in X ̶_{0}$ is defined by $z_{(t, x)} (τ, s) = z (t + τ, x + s)$ , $(τ, s) \in (- \infty, 0] \times [0, r]$ , and the phase space $X ̶_{0}$ satisfies suitable axioms. Using the method of bicharacteristics and the fixed-point method we prove a theorem on the local existence and uniqueness of Carathéodory solutions of the mixed problem.

Local generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in two independent variables

Jan Turo (1989)

Annales Polonici Mathematici

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Semilinear hyperbolic functional equations

László Simon (2014)

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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 some boundary value problems for a class of hyperbolic systems of second order in conic domains.

Kharibegashvili, S. (2005)

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Balachandran, K., Park, J.Y. (2002)

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Jan Turo (1999)

Annales Polonici Mathematici

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Local existence of generalized solutions to nonlocal problems for nonlinear functional partial differential equations of first order is investigated. The proof is based on the bicharacteristics and successive approximations methods.

On the local Cauchy problem for nonlinear hyperbolic functional differential equations

Tomasz Człapiński (1997)

Annales Polonici Mathematici

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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).

Global solvability of the mixed problem for first order functional partial differential equations

Jan Turo (1991)

Annales Polonici Mathematici

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Generalized Cauchy problems for hyperbolic functional differential systems

Elżbieta Puźniakowska-Gałuch (2014)

Annales Polonici Mathematici

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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.

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

Tomasz Człapiński (1997)

Annales Polonici Mathematici

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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.

Regularization method for parabolic equation with variable operator.

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On the existence of a classical solution of a mixed boundary problem for a second order one-dimensional hyperbolic equation. II.

Lažetić, Nebojša L. (1998)

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Noncharacteristic mixed problems for hyperbolic systems of the first order

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CONTENTS1. Introduction....................................................................................................................................................52. Notations and preliminaries .........................................................................................................................11 2.1. Function spaces and spaces of distributions............................................................................................11 2.2. Perturbations...