A strong solution of an evolution problem with integral conditions.

Mesloub, S.; Bouziani, A.; Kechkar, N.

Displaying similar documents to “A strong solution of an evolution problem with integral conditions.”

On uniqueness for a system of heat equations coupled in the boundary conditions.

Kordoš, M. (2004)

Acta Mathematica Universitatis Comenianae. New Series

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Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type.

Denche, M., Marhoune, A.L. (2001)

International Journal of Mathematics and Mathematical Sciences

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Higher integrability for weak solutions of higher order degenerate parabolic systems.

Bögelein, Verena (2008)

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A nonlinear heat equation with temperature-dependent parameters.

Rincon, M.A., Límaco, J., Liu, I-Shih (2006)

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Existence of solutions of the Cauchy problem for semilinear infinite systems of parabolic differential-functional equations.

Pudełko, Anna (2004)

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Solution to a transmission problem for quasilinear pseudoparabolic equations by the Rothe method.

Bouziani, A., Merazga, N. (2007)

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On a nonlocal boundary value problem for second-order nonlinear singular differential equations.

Lomtatidze, A., Malaguti, L. (2000)

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$L_{\infty}$ -estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski (1996)

Banach Center Publications

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Existence of weak solutions and an $L_{\infty}$ -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The $L_{\infty}$ -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.

Cauchy-Neumann problem for a class of nondiagonal parabolic systems with quadratic nonlinearities II. Local and global solvability results

Arina A. Arkhipova (2001)

Commentationes Mathematicae Universitatis Carolinae

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We prove local in time solvability of the nonlinear initial-boundary problem to nonlinear nondiagonal parabolic systems of equations (multidimensional case). No growth restrictions are assumed on generating the system functions. In the case of two spatial variables we construct the global in time solution to the Cauchy-Neumann problem for a class of nondiagonal parabolic systems. The solution is smooth almost everywhere and has an at most finite number of singular points.

$L_{\infty}$ -estimate for solutions of nonlinear parabolic systems

Wojciech Zajączkowski (1996)

Banach Center Publications

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We prove existence of weak solutions to nonlinear parabolic systems with p-Laplacians terms in the principal part. Next, in the case of diagonal systems an $L_{\infty}$ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, $L_{\infty}$ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The $L_{\infty}$ -estimates are obtained by the Di Benedetto methods.