PROBLEM WITH INTEGRAL CONDITION FOR A PARTIAL DIFFERENTIAL EQUATION OF THE FIRST ORDER WITH RESPECT TO TIME

P.I. Kalenyuk; I.V.Kohut; Z.M.Nytrebych

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PROBLEM WITH INTEGRAL CONDITION FOR A PARTIAL DIFFERENTIAL EQUATION OF THE FIRST ORDER WITH RESPECT TO TIME

机译：关于时间的一阶偏微分方程的积分条件问题

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We investigate the problem with inhomogeneous integral condition for a homogeneous partial differen tial equation of the first order with respect to time and, in the general case, of infinite order with respect to the space variable with constant coefficients. We prove the existence and uniqueness of a solution of the problem in a class of quasipolynomials of the special form. We construct a solution of this problem with the use of the differential-symbol method. In the case of existence of a nonunique solution of the problem, we propose formulas for the construction of a particular solution of the problem.

机译：我们研究一阶齐次偏微分方程关于时间的不均匀积分条件的问题，在一般情况下，对于具有恒定系数的空间变量来说是无限次的。我们用一类特殊形式的拟多项式证明了问题解的存在性和唯一性。我们使用差分符号方法构造了这个问题的解决方案。在存在问题的非唯一解的情况下，我们提出用于构造问题的特定解的公式。

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《Journal of Mathematical Sciences》 |2012年第3期|p.293-304|共12页
作者
P.I. Kalenyuk; I.V.Kohut; Z.M.Nytrebych;
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Institute of Applied Mathematics and Fundamental Sciences, "L'vivs'ka Politekhnika" National University, Lviv, Ukraine,Rzeszow University, Rzeszow, Poland;

Institute of Applied Mathematics and Fundamental Sciences, "L'vivs'ka Politekhnika" National University, Lviv, Ukraine;

Institute of Applied Mathematics and Fundamental Sciences, "L'vivs'ka Politekhnika" National University, Lviv, Ukraine;

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PROBLEM WITH INTEGRAL CONDITION FOR A PARTIAL DIFFERENTIAL EQUATION OF THE FIRST ORDER WITH RESPECT TO TIME

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