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Displaying similar documents to “Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form”

Semilinear hyperbolic functional equations

László Simon (2014)

Banach Center Publications

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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 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.

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.