Geodesic
A mixed problem for a system of first order differential equations with continuous potential
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 145-151.

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We study a mixed problem for a first order differential system with two independent variables and continuous potential when the initial condition is an arbitrary square summable vector-valued function. The corresponding spectral problem is the Dirac system. It sets the convergence almost everywhere of a formal decision, obtained by the Fourier method. It is shown that the sum of a formal decision is a generalized solution of a mixed problem, understood as the limit of classical solutions for the case of smooth approximation of the initial data of the problem. 
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M. Sh. Burlutskaya. A mixed problem for a system of first order differential equations with continuous potential. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 16 (2016) no. 2, pp. 145-151. http://geodesic.mathdoc.fr/item/ISU_2016_16_2_a3/

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