On Uniqueness Morawetz Problem for the Chaplygin Equation

Abstract

For the equationwhere yK(y) > 0 for y = 0) in D, bounded by a Jordan (non-selfintersecting) "elliptic" arc Γ (for > 0) with endpoints A(0, 0)and B(l, 0), l > 0, and for y < 0 by a characteristic γ 1 through A which meets the characteristic γ 2 through B at the points C, the uniqueness of the Morawetz problem is proved without assuming that Γ is monotone.

Some Properties and Applications of the RiemannHadamard Function of Darboux Problem for Telegraph Equation

“…It is well known that the Riemann--Hadamard function plays an important role in the study of problem D ; this function was defined and constructed in [1][2][3][4][5][6] for some special cases of Eq. (1).In this section, we present an in a sense modified (as compared with the approaches used in the above-mentioned papers) approach to defining the Riemann--Hadamard function of problem D for Eq.…”

“…(1).In this section, we present an in a sense modified (as compared with the approaches used in the above-mentioned papers) approach to defining the Riemann--Hadamard function of problem D for Eq. (1) in case if boundary values is defined on non-characteristic.…”