Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order

Jozef Kačur

Czechoslovak Mathematical Journal (1978)

  • Volume: 28, Issue: 4, page 507-524
  • ISSN: 0011-4642

How to cite

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Kačur, Jozef. "Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order." Czechoslovak Mathematical Journal 28.4 (1978): 507-524. <http://eudml.org/doc/13087>.

@article{Kačur1978,
author = {Kačur, Jozef},
journal = {Czechoslovak Mathematical Journal},
keywords = {Difference Approximation Method; Rothe's Method; Existence; Cauchy Problem; Approximate Solutions; First Initial Value Problem; Nonlinear Parabolic Equation},
language = {eng},
number = {4},
pages = {507-524},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order},
url = {http://eudml.org/doc/13087},
volume = {28},
year = {1978},
}

TY - JOUR
AU - Kačur, Jozef
TI - Method of Rothe and nonlinear parabolic boundary value problems of arbitrary order
JO - Czechoslovak Mathematical Journal
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 28
IS - 4
SP - 507
EP - 524
LA - eng
KW - Difference Approximation Method; Rothe's Method; Existence; Cauchy Problem; Approximate Solutions; First Initial Value Problem; Nonlinear Parabolic Equation
UR - http://eudml.org/doc/13087
ER -

References

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  1. J. Kačur, On existence of the weak solution for non-linear partial differential equations of elliptic type. I, Comment. Math. Univ. Carolinae, 11, 1 (1970), 137-181. (1970) Zbl0195.39503MR0301357
  2. J. Kačur, On existence of the weak solution for non-linear partial differential equations of elliptic type. II, Comment. Math. Univ. Carolinae, 13, 2 (1972), 211 - 225. (1972) Zbl0242.35031MR0308590
  3. K. Rektorys, On application of direct variational methods to the solution of parabolic boundary value problems of arbitrary order in the space variables, Czech. Math. Journal, 27 (96), (1971), 318-339. (1971) Zbl0217.41601MR0298237
  4. J. Nečas, Les méthodes directes en théorie des équations elliptiques, Prague, 1967. (1967) MR0227584
  5. J. Nečas, Les équations elliptiques non linéaires, L'école d'été, Tchécoslovaquie, 1967. Czech. Math. Journal 2 (1969), 252-274. (1967) Zbl0193.39202MR0252829
  6. E. Rothe, 10.1007/BF01782368, Math. ann. 102 (1930). (1930) Zbl56.1076.02DOI10.1007/BF01782368
  7. T. Д. Вентцель, Перваяа краевая задача для квазилинейново уравнения со многими пространственными переменными, Матем. сб. 41 (83), (1957), 499-520. (1957) Zbl0995.90594MR0089346
  8. О. А. Ладыженская, Решение в целом первой краевой задачи для квазилинейных параболических уравнений, ДАН СССР 107, (1965), 636-639. (1965) Zbl1099.01519
  9. А. М. Ильин А. С. Калашников О. А. Олейник, Линейные уравнения второго порядка параболического типа, УМН 17, вьш. 3, (1962), 3-146. (1962) Zbl1226.30001
  10. П. П. Мосолов, Вариационные методы в нестационарных задачах, (Параболический случай.) Изв. АН СССР, 34 (1970), 425-457. (1970) Zbl1170.92319MR0270245
  11. G. J. Мintу, On а ''monotonicity" method for the solution of nonlinear equation in Banach spaces, Proc. N.A.S. USA 50 (1963), 1038--1041. (1963) MR0162159
  12. F. E. Browder, Nonlinear elliptic boundary value problems, Bull. Amer, Math. Soc. 69, N. 6 (1963), 862-874. (1963) Zbl0127.31901MR0156116
  13. F. E. Browder, Strongly nonlinear parabolic boundary value problems, Amer. Journ. of Math. 86, 2 (1964). (1964) Zbl0143.33501
  14. M. A. Красносельский Я. Б. Рутицкий, Выпуклые функции и пространства Орлича Москва, 1958. 
  15. K. Yosida, Functional analysis, Springer-Verlag, 1965. (1965) Zbl0126.11504

Citations in EuDML Documents

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  1. Dana Lauerová, The Rothe method and time periodic solutions to the Navier-Stokes equations and equations of magnetohydrodynamics
  2. Emmanuel Kwame Essel, Komil Kuliev, Gulchehra Kulieva, Lars-Erik Persson, Homogenization of quasilinear parabolic problems by the method of Rothe and two scale convergence
  3. Jindřich Nečas, Application of Rothe's method to abstract parabolic equations
  4. Jozef Kačur, Stabilization of solutions of abstract parabolic equations
  5. Milan Pultar, Solutions of abstract hyperbolic equations by Rothe method.
  6. Marián Slodička, Parabolic partial differential equations with memory
  7. Igor Bock, Jozef Kačur, Application of Rothe's method to parabolic variational inequalities

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