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Monotone method for nonlineer nonlocal hyperbolic problems. (English) Zbl 1026.35072
The paper deals with a monotone iterative method for first-order hyperbolic initial-boundary value problem which involve nonlocal terms. The authors introduce a new definition of lower and upper solution in order to overcome some difficulties for application of the comparison principle. Two monotone sequences of upper and lower solutions are constructed which converge in an appropriate functional space to the unique solution of the problem under consideration.
MSC:
35L60 First-order nonlinear hyperbolic equations
35A35 Theoretical approximation in context of PDEs
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