| Title:
|
Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space (English) |
| Author:
|
Slodička, Marián |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
34 |
| Issue:
|
6 |
| Year:
|
1989 |
| Pages:
|
439-448 |
| Summary lang:
|
English |
| Summary lang:
|
Russian |
| Summary lang:
|
Czech |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Rothe-Galerkin method is used for discretization. The rate of convergence in $C(I, L_p(G))$ for the approximate solution of a quasilinear parabolic equation with a Volterra operator on the right-hand side is established. (English) |
| Keyword:
|
error estimate |
| Keyword:
|
Rothe’s method |
| Keyword:
|
semidiscretization in time |
| Keyword:
|
quasilinear parabolic Volterra integro-differential equation |
| Keyword:
|
rate of convergence |
| Keyword:
|
galerkin's method |
| MSC:
|
35K22 |
| MSC:
|
45K05 |
| MSC:
|
45L05 |
| MSC:
|
49K22 |
| MSC:
|
65M15 |
| MSC:
|
65M20 |
| MSC:
|
65R20 |
| idZBL:
|
Zbl 0695.65087 |
| idMR:
|
MR1026508 |
| DOI:
|
10.21136/AM.1989.104374 |
| . |
| Date available:
|
2008-05-20T18:37:49Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104374 |
| . |
| Reference:
|
[1] P. G. Ciarlet: The finite element method for elliptic problems.North. Holland, Amsterdam 1978. Zbl 0383.65058, MR 0520174 |
| Reference:
|
[2] J. Descloux: Basic properties of Sobolev spaces, approximation by finite elements.Ecole polytechnique féderale Lausanne, Switzerland 1975. |
| Reference:
|
[3] G. Di Blasio: Linear parabolic evolution equations in $L_p$-spaces.Ann. Mat. Рurа Appl. 138 (1984), 55-104. MR 0779538, 10.1007/BF01762539 |
| Reference:
|
[4] R. Glowinski J. L. Lions R. Tremolieres: Analyse numerique des inequations variationelles.Dunod, Paris 1976. |
| Reference:
|
[5] D. Henry: Geometric theory of semilinear parabolic equations.Springer-Verlag, Berlin - Heidelberg-New York 1981. Zbl 0456.35001, MR 0610244 |
| Reference:
|
[6] J. Kačur: Application of Rothe's method to evolution integrodifferential equations.Universität Heidelberg, SFB 123, 381, 1986. |
| Reference:
|
[7] J. Kačur: Method or Rothe in evolution equations.Teubner Texte zur Mathematik 80, Leipzig 1985. MR 0834176 |
| Reference:
|
[8] A. Kufner O. John S. Fučík: Function spaces.Academia, Prague 1977. MR 0482102 |
| Reference:
|
[9] M. Marino A. Maugeri: $L_p$-theory and partial Hölder continuity for quasilinear parabolic systems of higher order with strictly controlled growth.Ann. Mat. Рurа Appl. 139 (1985), 107-145. MR 0798171, 10.1007/BF01766852 |
| Reference:
|
[10] V. Pluschke: Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method.(to appear in Czechoslovak. Math. J.). Zbl 0671.35037, MR 0962908 |
| Reference:
|
[11] K. Rektorys: The method of discretization in time and and partial differential equations.D. Reidel. Publ. Do., Dordrecht-Boston-London 1982. MR 0689712 |
| Reference:
|
[12] Ch. G. Simander: On Dirichlet's boundary value problem.Lecture Notes in Math. 268, Springer-Verlag, Berlin-Heidelberg-New York 1972. |
| Reference:
|
[13] M. Slodička: An investigation of convergence and error estimate of approximate solution for quasiliriear integrodifferential equation.(to appear). |
| Reference:
|
[14] W. von Wahl: The equation $u' + A(t) u = f$ in a Hilbert space and $L_p$-estimates for parabolic equations.J. London Math. Soc. 25 (1982), 483 - 497. Zbl 0493.35050, MR 0657505, 10.1112/jlms/s2-25.3.483 |
| Reference:
|
[15] V. Thomee: Galerkin finite element method for parabolic problems.Lecture Notes in Math. 1054, Springer-Verlag, Berlin -Heidelberg-New York-Tokyo 1984. MR 0744045 |
| Reference:
|
[16] M. F. Wheeler: A priori $L_2$-error estimates for Galerkin approximations to parabolic partial differential equations.SIAM. J. Numer. Anal. 10 (1973), 723 - 759. MR 0351124, 10.1137/0710062 |
| . |
