Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_p$-space

Marián Slodička

Smoothing effect and regularity for evolution integrodifferential systems

Marián Slodička (1989)

Commentationes Mathematicae Universitatis Carolinae

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The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition

Volker Pluschke, Frank Weber (1999)

Commentationes Mathematicae Universitatis Carolinae

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We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition $- \partial u / \partial ν_{A} = g (\cdot, \cdot, u)$ with a locally defined, $L_{r}$ -bounded function $g (t, \cdot, ξ)$ . We prove the existence of a local weak solution to the problem by means of the Rothe method. A uniform a priori estimate for the Rothe approximations in $L_{\infty}$ , which is required by the assumptions on $g$ , is derived...

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On approximate solutions of degenerate integrodifferential parabolic problems

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Displaying similar documents to “Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the L p -space”

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Displaying similar documents to “Error estimate of approximate solution for a quasilinear parabolic integrodifferential equation in the $L_{p}$ -space”