On boundary-value problems for partial differential equations of order higher than two

Jan Popiołek

Annales Polonici Mathematici (1997)

  • Volume: 65, Issue: 2, page 139-150
  • ISSN: 0066-2216

Abstract

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We prove the existence of solutions of some boundary-value problems for partial differential equations of order higher than two. The general idea is similar to that in [1]. We make an essential use of the results of our paper [12].

How to cite

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Jan Popiołek. "On boundary-value problems for partial differential equations of order higher than two." Annales Polonici Mathematici 65.2 (1997): 139-150. <http://eudml.org/doc/270020>.

@article{JanPopiołek1997,
abstract = {We prove the existence of solutions of some boundary-value problems for partial differential equations of order higher than two. The general idea is similar to that in [1]. We make an essential use of the results of our paper [12].},
author = {Jan Popiołek},
journal = {Annales Polonici Mathematici},
keywords = {partial differential equation; boundary-value problem; Volterra integral equation; initial boundary value problem},
language = {eng},
number = {2},
pages = {139-150},
title = {On boundary-value problems for partial differential equations of order higher than two},
url = {http://eudml.org/doc/270020},
volume = {65},
year = {1997},
}

TY - JOUR
AU - Jan Popiołek
TI - On boundary-value problems for partial differential equations of order higher than two
JO - Annales Polonici Mathematici
PY - 1997
VL - 65
IS - 2
SP - 139
EP - 150
AB - We prove the existence of solutions of some boundary-value problems for partial differential equations of order higher than two. The general idea is similar to that in [1]. We make an essential use of the results of our paper [12].
LA - eng
KW - partial differential equation; boundary-value problem; Volterra integral equation; initial boundary value problem
UR - http://eudml.org/doc/270020
ER -

References

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  1. [1] E. A. Baderko, On solvability of boundary-value problems for parabolic equations of higher order in curvilinear domains, Differentsial'nye Uravneniya 12 (1976), 1782-1792 (in Russian). 
  2. [2] Z. D. Dubl'a, Boundary-value problems for differential equations in unbounded domains, Differentsial'nye Uravneniya 10 (1974), 159-161 (in Russian). 
  3. [3] Z. D. Dubl'a, On the Dirichlet problem for a class of equations of third order, Differentsial'nye Uravneniya 13 (1977), 50-55 (in Russian). 
  4. [4] T. D. Dzhuraev, Boundary-Value Problems for Equations of Mixed and Mixed-Composite Types, FAN, Tashkent, 1979 (in Russian). 
  5. [5] T. D. Dzhuraev and M. Mamazhanov, On a class of boundary-value problems for equations of third order containing the operator of heat conduction, Izv. Akad. Nauk UzSSR 1985 (2), 22-26 (in Russian). Zbl0615.35058
  6. [6] M. Hanin, Propagation of an aperiodic wave in a compressible viscous medium, J. Math. Phys. 36 (1957), 133-150. 
  7. [7] L. I. Kamynin, The method of heat potentials for parabolic equations with discontinuous coefficients, Sibirsk. Mat. Zh. 4 (1963), 1071-1105 (in Russian). 
  8. [8] R. Nardini, Soluzione di un problema al contorno della magneto-idrodinamica, Ann. Mat. Pura Appl. 35 (1953), 269-290. Zbl0051.23801
  9. [9] R. Nardini, Sul comportamento asintotico della soluzione di un problema al contorno della magneto-idrodinamica, Rend. Accad. Naz. Lincei 16 (1954), 225-231, 341-348, 365-366. Zbl0058.42404
  10. [10] B. Pini, Un problema di valori al contorno per un'equazione a derivate parziali del terzo ordine con parte principale di tipo composito, Rend. Sem. Fac. Sci. Univ. Cagliari 27 (1957), 114-135. Zbl0083.32303
  11. [11] J. Popiołek, The Cauchy problem for a higher-order partial differential equation, Izv. Akad. Nauk UzSSR 1 (1989), 25-30 (in Russian). 
  12. [12] J. Popiołek, Properties of some integrals related to partial differential equations of order higher than two, this issue, 129-138. Zbl0887.35033
  13. [13] A. S. Rustamov, A mixed problem for the equation of composite type with variable coefficients, Differentsial'nye Uravneniya 18 (1982), 1794-1804 (in Russian). Zbl0512.35060
  14. [14] S. N. Salikhov, On a boundary-value problem for a partial differential equation with multiple characteristics, Izv. Akad. Nauk UzSSR 1983 (5), 29-33 (in Russian). Zbl0566.35022
  15. [15] Ya. S. Sharifbaev, On some boundary-value problems for equations of third order with the heat conduction operator in the principal part, Izv. Akad. Nauk UzSSR 1975 (1), 45-48 (in Russian). 
  16. [16] J. Urbanowicz, On a certain non-linear contact problem for a one-dimensional parabolic equation of second order, Demonstratio Math. 16 (1983), 61-83. Zbl0545.35047
  17. [17] S. S. Vojt, Propagation of initial waves in a viscous gas, Uchen. Zap. MTU 172 (1954), 125-142 (in Russian). 

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