Modified Problems for Euler–Darboux Equations with Parameters with Absolute Values Equal to $$ \frac{1}{2} $$
نویسندگان
چکیده
We consider the Euler–Darboux equation with parameters such that their absolute values are equal to $$ \frac{1}{2} . Since Cauchy problem in classical formulation is ill-posed for of parameters, we propose formulations and solutions modified Cauchy-type problems following parameters: (a) \alpha =\beta =\frac{1}{2}; (b) =-\frac{1}{2}\ \mathrm{and}\ \beta (c) =-\frac{1}{2}. In case (a), solved by Riemann method. use obtained result formulate analog Δ1 first quadrant translated boundary conditions on axes nonstandard conjunction singularity line coefficients y = x. The condition gluing normal derivatives solution second one contains limit a combination its derivatives. reduced uniquely solvable system integral equations.
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ژورنال
عنوان ژورنال: Journal of Mathematical Sciences
سال: 2022
ISSN: ['1072-3374', '1573-8795']
DOI: https://doi.org/10.1007/s10958-022-06040-2