Displaying similar documents to “Global solvability of the mixed problem for first order functional partial differential equations”

Infinite systems of first order PFDEs with mixed conditions

W. Czernous (2008)

Annales Polonici Mathematici

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We consider mixed problems for infinite systems of first order partial functional differential equations. An infinite number of deviating functions is permitted, and the delay of an argument may also depend on the spatial variable. A theorem on the existence of a solution and its continuous dependence upon initial boundary data is proved. The method of successive approximations is used in the existence proof. Infinite differential systems with deviated arguments and differential integral...

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.