On the Cauchy problem for hyperbolic functional-differential equations

• Autorzy: Adrian Karpowicz , Henryk Leszczyński
• Języki publikacji: EN

Abstrakty

EN

We consider the Cauchy problem for a nonlocal wave equation in one dimension. We study the existence of solutions by means of bicharacteristics. The existence and uniqueness is obtained in $W^{1,∞}_{loc}$ topology. The existence theorem is proved in a subset generated by certain continuity conditions for the derivatives.

Kategorie tematyczne

• 35L71: Semilinear second-order hyperbolic equations
• 35A01: Existence problems: global existence, local existence, non-existence
• 35R10: Partial functional-differential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2015
• Tom: 115
• Numer: 1
• Strony: 53-74

Daty

wydano

2015

Twórcy

autor

Adrian Karpowicz

• Institute of Mathematics, University of Gdańsk, 80-952 Gdańsk, Poland

autor

Henryk Leszczyński

• Institute of Mathematics, University of Gdańsk, 80-952 Gdańsk, Poland

Identyfikatory

DOI

10.4064/ap115-1-5