Displaying similar documents to “Some properties of solutions for the generalized thin film equation in one space dimension.”

L ∞ -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 ∞ -estimate for weak solutions is shown under additional restrictive growth conditions. Finally, L ∞ -estimates for weakly nondiagonal systems (where nondiagonal elements are absorbed by diagonal ones) are proved. The L ∞ -estimates are obtained by the Di Benedetto methods.

L ∞ -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 ∞ -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The L ∞ -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.

Qualitative investigation of nonlinear differential equations describing infiltration of water

Xingbao Wu (1995)

Annales Polonici Mathematici

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A nonlinear differential equation of the form (q(x)k(x)u')' = F(x,u,u') arising in models of infiltration of water is considered, together with the corresponding differential equation with a positive parameter λ, (q(x)k(x)u')' = λF(x,u,u'). The theorems about existence, uniqueness, boundedness of solution and its dependence on the parameter are established.