$L_∞$-estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski

Displaying similar documents to “ $L_{\infty}$ -estimates for solutions of nonlinear parabolic systems with gradient linear growth”

$L_{\infty}$ -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.

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

Bögelein, Verena (2008)

Annales Academiae Scientiarum Fennicae. Mathematica

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

Pudełko, Anna (2004)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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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.

On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions

Joachim Naumann, Jörg Wolf, Michael Wolff (1998)

Commentationes Mathematicae Universitatis Carolinae

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We prove the interior Hölder continuity of weak solutions to parabolic systems $\frac{\partial u^{j}}{\partial t} - D_{α} a_{j}^{α} (x, t, u, \nabla u) = 0 in Q (j = 1, ..., N)$ ( $Q = Ω \times (0, T), Ω \subset ℝ^{2}$ ), where the coefficients $a_{j}^{α} (x, t, u, ξ)$ are measurable in $x$ , Hölder continuous in $t$ and Lipschitz continuous in $u$ and $ξ$ .

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

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

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

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Regularizing a nonlinear integroparabolic Fokker--Planck equation with space-periodic solutions: existence of strong solutions.

Lavrent&amp;#039;ev, M.M.jun., Spigler, R., Akhmetov, D.R. (2001)

Sibirskij Matematicheskij Zhurnal

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Growth of the product $\prod_{j = 1}^{n} (1 - x^{a_{j}})$

J. P. Bell, P. B. Borwein, L. B. Richmond (1998)

Acta Arithmetica

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We estimate the maximum of $\prod_{j = 1}^{n} | 1 - x^{a_{j}} |$ on the unit circle where 1 ≤ a₁ ≤ a₂ ≤ ... is a sequence of integers. We show that when $a_{j}$ is $j^{k}$ or when $a_{j}$ is a quadratic in j that takes on positive integer values, the maximum grows as exp(cn), where c is a positive constant. This complements results of Sudler and Wright that show exponential growth when $a_{j}$ is j. In contrast we show, under fairly general conditions, that the maximum is less than $2^{n} / n^{r}$ , where r is an arbitrary positive number. One consequence...

Displaying similar documents to “ L ∞ -estimates for solutions of nonlinear parabolic systems with gradient linear growth”

Displaying similar documents to “ $L_{\infty}$ -estimates for solutions of nonlinear parabolic systems with gradient linear growth”