Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space
Slodička, Marián
Applications of Mathematics, Tome 34 (1989), p. 439-448 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1989-01-01
Classification:  35K22,  45K05,  45L05,  49K22,  65M15,  65M20,  65R20 
@article{104374,
     author = {Mari\'an Slodi\v cka},
     title = {Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L\_p$-space},
     journal = {Applications of Mathematics},
     volume = {34},
     year = {1989},
     pages = {439-448},
     zbl = {0695.65087},
     mrnumber = {1026508},
     language = {en},
     url = {http://dml.mathdoc.fr/item/104374}
}

Slodička, Marián. Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space. Applications of Mathematics, Tome 34 (1989) pp. 439-448. http://gdmltest.u-ga.fr/item/104374/

P. G. Ciarlet The finite element method for elliptic problems, North. Holland, Amsterdam 1978. (1978) | MR 0520174 | Zbl 0383.65058

J. Descloux Basic properties of Sobolev spaces, approximation by finite elements, Ecole polytechnique féderale Lausanne, Switzerland 1975. (1975)

G. Di Blasio Linear parabolic evolution equations in $L_p$-spaces, Ann. Mat. Рurа Appl. 138 (1984), 55-104. (1984) | Article | MR 0779538

R. Glowinski J. L. Lions R. Tremolieres Analyse numerique des inequations variationelles, Dunod, Paris 1976. (1976)

D. Henry Geometric theory of semilinear parabolic equations, Springer-Verlag, Berlin - Heidelberg-New York 1981. (1981) | MR 0610244 | Zbl 0456.35001

J. Kačur Application of Rothe's method to evolution integrodifferential equations, Universität Heidelberg, SFB 123, 381, 1986. (1986)

J. Kačur Method or Rothe in evolution equations, Teubner Texte zur Mathematik 80, Leipzig 1985. (1985) | MR 0834176

A. Kufner O. John S. Fučík Function spaces, Academia, Prague 1977. (1977) | MR 0482102

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. (1985) | Article | MR 0798171

V. Pluschke Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method, (to appear in Czechoslovak. Math. J.). | MR 0962908 | Zbl 0671.35037

K. Rektorys The method of discretization in time and and partial differential equations, D. Reidel. Publ. Do., Dordrecht-Boston-London 1982. (1982) | MR 0689712

Ch. G. Simander On Dirichlet's boundary value problem, Lecture Notes in Math. 268, Springer-Verlag, Berlin-Heidelberg-New York 1972. (1972)

M. Slodička An investigation of convergence and error estimate of approximate solution for quasiliriear integrodifferential equation, (to appear).

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. (1982) | Article | MR 0657505 | Zbl 0493.35050

V. Thomee Galerkin finite element method for parabolic problems, Lecture Notes in Math. 1054, Springer-Verlag, Berlin -Heidelberg-New York-Tokyo 1984. (1984) | MR 0744045

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. (1973) | Article | MR 0351124