Geodesic
Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space
Applications of Mathematics, Tome 34 (1989) no. 6, pp. 439-448
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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.
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.
DOI : 10.21136/AM.1989.104374
Classification : 35K22, 45K05, 45L05, 49K22, 65M15, 65M20, 65R20
Keywords: error estimate; Rothe’s method; semidiscretization in time; quasilinear parabolic Volterra integro-differential equation; rate of convergence; galerkin's method 
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Slodička, Marián. Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space. Applications of Mathematics, Tome 34 (1989) no. 6, pp. 439-448. doi: 10.21136/AM.1989.104374

[1] P. G. Ciarlet: The finite element method for elliptic problems. North. Holland, Amsterdam 1978. | MR | Zbl

[2] J. Descloux: Basic properties of Sobolev spaces, approximation by finite elements. Ecole polytechnique féderale Lausanne, Switzerland 1975.

[3] G. Di Blasio: Linear parabolic evolution equations in $L_p$-spaces. Ann. Mat. Рurа Appl. 138 (1984), 55-104. | DOI | MR

[4] R. Glowinski J. L. Lions R. Tremolieres: Analyse numerique des inequations variationelles. Dunod, Paris 1976.

[5] D. Henry: Geometric theory of semilinear parabolic equations. Springer-Verlag, Berlin - Heidelberg-New York 1981. | MR | Zbl

[6] J. Kačur: Application of Rothe's method to evolution integrodifferential equations. Universität Heidelberg, SFB 123, 381, 1986.

[7] J. Kačur: Method or Rothe in evolution equations. Teubner Texte zur Mathematik 80, Leipzig 1985. | MR

[8] A. Kufner O. John S. Fučík: Function spaces. Academia, Prague 1977. | MR

[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. | DOI | MR

[10] V. Pluschke: Local solution of parabolic equations with strongly increasing nonlinearity by the Rothe method. (to appear in Czechoslovak. Math. J.). | MR | Zbl

[11] K. Rektorys: The method of discretization in time and and partial differential equations. D. Reidel. Publ. Do., Dordrecht-Boston-London 1982. | MR

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

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

[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. | DOI | MR | Zbl

[15] V. Thomee: Galerkin finite element method for parabolic problems. Lecture Notes in Math. 1054, Springer-Verlag, Berlin -Heidelberg-New York-Tokyo 1984. | MR

[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. | DOI | MR

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