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The third mixed problem for the Sonin equation in a half space

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Ukrainian Mathematical Journal Aims and scope

Abstract

We consider follwing mixed boundary-value problem:

$$\begin{array}{*{20}c} {u'_t (t,R) + xu'_y (t,R) + yu'_z (t,R) = u''_{x^2 } (t,R) + f(t,R)} \\ {in \Pi _T = \{ (t,R),0< t \leqslant T,R = (x,y,z),R \in E_3 ,0< x\} ,} \\ {u(0,R) = u_0 (R),u'_x (t,0,y,z) + \beta (t)u(t,0,y,z) = g(t,y,z).} \\ \end{array}$$

A solution of this problem is obtained in the form of a potential.

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References

  1. A. Fridman,Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ (1964).

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  3. A. P. Malitskaya, “The first mixed problem for the Sonin equation in a half space,”Ukr. Mat. Zh.,35, No. 3, 321–326 (1983).

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Authors and Affiliations

  1. Ivano-Frankovsk Pedagogical Institute, Ivano-Frankovsk

    A. P. Malitskaya

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  1. A. P. Malitskaya
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1109–1114, August, 1993.

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Malitskaya, A.P. The third mixed problem for the Sonin equation in a half space. Ukr Math J 45, 1236–1243 (1993). https://doi.org/10.1007/BF01070971

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  • DOI: https://doi.org/10.1007/BF01070971

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