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$L^{2}$ -error estimates of the extrapolated Crank-Nicolson discontinuous Galerkin approximations for nonlinear Sobolev equations.

Ohm, Mi Ray, Lee, Hyun Young, Shin, Jun Yong (2010)

Journal of Inequalities and Applications [electronic only]

$L^{2}$ -preserving Schrödinger heat flow under the Ricci flow.

Wang, Linfeng (2010)

Balkan Journal of Geometry and its Applications (BJGA)

$L^{2}$ -stability of multi-solitons

Claudio Muñoz (2011/2012)

Séminaire Laurent Schwartz — EDP et applications

The aim of this note is to give a short review of our recent work (see [5]) with Miguel A. Alejo and Luis Vega, concerning the $L^{2}$ -stability, and asymptotic stability, of the $N$ -soliton of the Korteweg-de Vries (KdV) equation.

$L^{2}$ -stability of the solutions to a nonlinear binary reaction-diffusion system of P.D.E.s

Salvatore Rionero (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The $L^{2}$ -stability (instability) of a binary nonlinear reaction diffusion system of P.D.E.s - either under Dirichlet or Neumann boundary data - is considered. Conditions allowing the reduction to a stability (instability) problem for a linear binary system of O.D.E.s are furnished. A peculiar Liapunov functional $V$ linked (together with the time derivative along the solutions) by direct simple relations to the eigenvalues, is used.

$L_{\infty}$ -convergence of finite element Galerkin approximations for parabolic problems

Joachim A. Nitsche (1979)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

$L_{\infty}$ -estimate for qualitatively bounded weak solutions of nonlinear degenerate diagonal parabolic systems.

Zaja̧czkowski, W.M. (1996)

Journal of Applied Analysis

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

Wojciech Zajączkowski (1996)

Banach Center Publications

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.

$L^{\infty}$ -estimates for nonlinear parabolic equations with natural growth conditions

Vincenzo Vespri (1993)

Rendiconti del Seminario Matematico della Università di Padova

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

Wojciech Zajączkowski (1996)

Banach Center Publications

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.

$L^{\infty}$ estimates of solution for $m$ -Laplacian parabolic equation with a nonlocal term

Pulun Hou, Caisheng Chen (2011)

Czechoslovak Mathematical Journal

In this paper, we consider the global existence, uniqueness and $L^{\infty}$ estimates of weak solutions to quasilinear parabolic equation of $m$ -Laplacian type $u_{t} - {div (| \nabla u |}^{m - 2} {\nabla u) = u | u |}^{β - 1} \int_{Ω} {| u |}^{α} d x$ in $Ω \times (0, \infty)$ with zero Dirichlet boundary condition in $\partial Ω$ . Further, we obtain the $L^{\infty}$ estimate of the solution $u (t)$ and $\nabla u (t)$ for $t > 0$ with the initial data $u_{0} \in L^{q} (Ω)$ $(q > ...$

$L^{p}$ -decay of solutions to dissipative-dispersive perturbations of conservation laws

Grzegorz Karch (1997)

Annales Polonici Mathematici

We study the decay in time of the spatial $L^{p}$ -norm (1 ≤ p ≤ ∞) of solutions to parabolic conservation laws with dispersive and dissipative terms added uₜ - uₓₓₜ - νuₓₓ + buₓ = f(u)ₓ or uₜ + uₓₓₓ - νuₓₓ + buₓ = f(u)ₓ, and we show that under general assumptions about the nonlinearity, solutions of the nonlinear equations have the same long time behavior as their linearizations at the zero solution.

$L_{p}$ -estimates for solutions of Dirichlet and Neumann problems to heat equation in the wedge with edge of arbitrary codimension

Nazarov, Alexander I. (2002)

Equadiff 10

$L^{p}$ regularity for weak solutions of parabolic systems

Sergio Campanato (1980)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

$L^{p}$ -spectrum of Ornstein-Uhlenbeck operators

Giorgio Metafune (2001)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

La diffusione del calore in uno strato di spessore variabile in presenza di scambi termici non lineari con l'ambiente. (I) Deduzione di limitazioni a priori sulla temperatura e le sue derivate

Antonio Fasano, Mario Primicerio (1973)

Rendiconti del Seminario Matematico della Università di Padova

La méthode des caractéristiques pour les problèmes de convection-diffusion stationnaires

A. Bermúdez, J. Durany (1987)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Lagrangian and moving mesh methods for the convection diffusion equation

Konstantinos Chrysafinos, Noel J. Walkington (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [Chrysafinos and Walkington, SIAM J. Numer. Anal. 43 (2006) 2478–2499; Chrysafinos and Walkington, SIAM J. Numer. Anal. 44 (2006) 349–366] and the dependence of various constants upon the diffusion parameter is ...

Lagrangian evolution approach to surface-patch quadrangulation

Martin Húska, Matej Medl'a, Karol Mikula, Serena Morigi (2021)

Applications of Mathematics

We present a method for the generation of a pure quad mesh approximating a discrete manifold of arbitrary topology that preserves the patch layout characterizing the intrinsic object structure. A three-step procedure constitutes the core of our approach which first extracts the patch layout of the object by a topological partitioning of the digital shape, then computes the minimal surface given by the boundaries of the patch layout (basic quad layout) and then evolves it towards the object boundaries....

Laplace asymptotics for generalized K.P.P. equation

Jean-Philippe Rouquès (2010)

ESAIM: Probability and Statistics

Consider a one dimensional nonlinear reaction-diffusion equation (KPP equation) with non-homogeneous second order term, discontinuous initial condition and small parameter. For points ahead of the Freidlin-KPP front, the solution tends to 0 and we obtain sharp asymptotics (i.e. non logarithmic). Our study follows the work of Ben Arous and Rouault who solved this problem in the homogeneous case. Our proof is probabilistic, and is based on the Feynman-Kac formula and the large deviation principle...

Laplace asymptotics for generalized K.P.P. equation

Jean-Philippe Rouques (1997)

ESAIM: Probability and Statistics

Currently displaying 1 – 20 of 95

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