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Sfruttando i risultati di [1], si prova che le derivate spaziali $D^{\alpha}u$ di ordine $|\alpha|$ con $|\alpha|<m-1$ delle soluzioni in $Q$ di un sistema parabolico quasilineare di ordine $2m$ con andamenti strettamente controllati, sono parzialmente hölderiane in $Q$ con esponente di hölderianità decrescente al crescere di $|\alpha|$ .

Partial Hölder continuity of solutions of quasilinear parabolic systems of second order with linear growth

Sergio Campanato (1981)

Rendiconti del Seminario Matematico della Università di Padova

Partial Hölder continuity of the spatial derivatives of the solutions to nonlinear parabolic systems with quadratic growth

Mario Marino, Antonino Maugeri (1986)

Rendiconti del Seminario Matematico della Università di Padova

Periodic parabolic problems with nonlinearities indefinite in sign.

Tomás Godoy, Uriel Kaufmann (2007)

Publicacions Matemàtiques

Let Ω ⊂ RN be a smooth bounded domain. We give sufficient conditions (which are also necessary in many cases) on two nonnegative functions a, b that are possibly discontinuous and unbounded for the existence of nonnegative solutions for semilinear Dirichlet periodic parabolic problems of the form Lu = λa (x, t) up - b (x, t) uq in Ω × R, where 0 < p, q < 1 and λ > 0. In some cases we also show the existence of solutions uλ in the interior of the positive cone and that uλ can...

Periodic problems and problems with discontinuities for nonlinear parabolic equations

Tiziana Cardinali, Nikolaos S. Papageorgiou (2000)

Czechoslovak Mathematical Journal

In this paper we study nonlinear parabolic equations using the method of upper and lower solutions. Using truncation and penalization techniques and results from the theory of operators of monotone type, we prove the existence of a periodic solution between an upper and a lower solution. Then with some monotonicity conditions we prove the existence of extremal solutions in the order interval defined by an upper and a lower solution. Finally we consider problems with discontinuities and we show that...

Periodic solutions of evolution $m$ -Laplacian equations with a nonlinear convection term.

Liu, Wenjun (2007)

International Journal of Mathematics and Mathematical Sciences

Periodic solutions of quasilinear equations with discontinuous perturbations.

Crema, Janete, Boldrini, José Luiz (2000)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation

Leopold Herrmann (1985)

Czechoslovak Mathematical Journal

Periodic Solutions to a Parabolic Equation with Hysteresis.

Pavel Krejci (1987)

Mathematische Zeitschrift

Periodic trajectories for evolution equations in Banach spaces.

Voisei, Mircea D. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Periodic traveling waves for a nonlocal integro-differential model.

Bates, Peter, Chen, Fengxin (1999)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Perona-Malik equation: properties of explicit finite volume scheme

Angela Handlovičová (2007)

Kybernetika

The Perona–Malik nonlinear parabolic problem, which is widely used in image processing, is investigated in this paper from the numerical point of view. An explicit finite volume numerical scheme for this problem is presented and consistency property is proved.

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