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Some Pseudoparabolic Variational Inequalities with Higher Derivatives

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Abstract

We consider a pseudoparabolic variational inequality with higher derivatives. We prove the existence and uniqueness of a solution of this inequality with a zero initial condition.

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REFERENCES

  1. G. I. Barenblat, Yu. P. Zheltov, and T. N. Kochina, “On main concepts of the theory of filtration of homogeneous liquids in fissured rocks,” Prikl. Mat. Mekh., 24, Issue 5, 852–864 (1960).

    Google Scholar 

  2. L. I. Rubinshtein, “On the problem of heat propagation in heterogeneous media,” Izv. Akad. Nauk SSSR, Ser. Geogr. Geofiz., 12, No. 1, 27–45 (1948).

    Google Scholar 

  3. E. Di Benedetto and R. E. Showalter, “A pseudoparabolic variational inequality and Stefan problem,” Nonlin. Anal. Theory Meth. Appl., 6, No. 3, 279–291 (1982).

    Google Scholar 

  4. F. Scarpini, “General and pseudoparabolic variational inequalities: Approximate solutions,” Numer. Funct. Anal. Optiz., 9, 859–879 (1987).

    Google Scholar 

  5. H. Brill, Cauchy Probleme für nichtlineare parabolische und pseudoparabolische Gleichungen, Diss. dokt. naturwiss., Abt. Math., Ruhr-uni., Bochum (1974).

    Google Scholar 

  6. T. W. Ting, “Parabolic and pseudoparabolic partial differential equations,” J. Math. Soc. Japan, 21, No. 3, 440–453 (1969).

    Google Scholar 

  7. S. A. Gal'pern, “Cauchy problem for general systems of linear partial differential equations,” Dokl. Akad. Nauk SSSR, 119, No. 4, 640–643 (1958).

    Google Scholar 

  8. W. H. Ford, “Galerkin approximation to nonlinear pseudoparabolic partial differential equations,” Aequet. Math., 14, No. 3, 271–291 (1976).

    Google Scholar 

  9. M. O. Bas and S. P. Lavrenyuk, “On the uniqueness of a solution of the Fourier problem for a system of Sobolev–Gal'pern type,” Ukr. Mat. Zh., 48, No. 1, 124–128 (1996).

    Google Scholar 

  10. S. P. Lavrenyuk and M. B. Ptashnyk, “On certain nonlinear pseudoparabolic variational inequalities without initial conditions,” Ukr. Mat. Zh., 51, No. 3, 328–337 (1999).

    Google Scholar 

  11. V. G. Maz'ya, Sobolev Spaces [in Russian], Leningrad University, Leningrad (1985).

    Google Scholar 

  12. H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen [Russian translation], Mir, Moscow (1978).

    Google Scholar 

  13. J.-L. Lions, Quelques Méthodes de Resolution des Problèmes aux Limites Non Linéaires [Russian translation], Nauka, Moscow (1972).

    Google Scholar 

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Authors and Affiliations

  1. Lviv National University, Lviv

    M. B. Ptashnyk

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  1. M. B. Ptashnyk
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Ptashnyk, M.B. Some Pseudoparabolic Variational Inequalities with Higher Derivatives. Ukrainian Mathematical Journal 54, 112–125 (2002). https://doi.org/10.1023/A:1019749721158

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