Results 41 to 50 of about 1,966 (104)
Hölder gradient estimates for a class of singular or degenerate parabolic equations
Advances in Nonlinear Analysis, 2017 We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic ...
Imbert Cyril +2 more
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Analyticity of dissipative-dispersive systems in higher dimensions
, 2018 We investigate the analyticity of the attractors of a class of Kuramoto-Sivashinsky type pseudo-differential equations in higher dimensions, which are periodic in all spatial variables and possess a universal attractor.
Evripidou, Charalampos +1 more
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Advances in Nonlinear AnalysisWe consider the homogeneous Dirichlet problem for the parabolic equation ut−div(∣∇u∣p(x,t)−2∇u)=f(x,t)+F(x,t,u,∇u){u}_{t}-{\rm{div}}({| \nabla u| }^{p\left(x,t)-2}\nabla u)=f\left(x,t)+F\left(x,t,u,\nabla u) in the cylinder QT≔Ω×(0,T){Q}_{T}:= \Omega ...
Arora Rakesh, Shmarev Sergey
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The higher integrability of weak solutions of porous medium systems
Advances in Nonlinear Analysis, 2018 In this paper we establish that the gradient of weak solutions to porous medium-type systems admits the self-improving property of higher integrability.
Bögelein Verena +3 more
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H\"{o}lder continuity of solutions to the kinematic dynamo equations
, 2014 We study the propagation of regularity of solutions to a three dimensional system of linear parabolic PDE known as the kinematic dynamo equations. The divergence free drift velocity is assumed to be at the critical regularity level with respect to the ...
Friedlander, Susan, Suen, Anthony
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Dirichlet problem for quasi-linear elliptic equations
Electronic Journal of Differential Equations, 2002 We study the Dirichlet Problem associated to the quasilinear elliptic problem $$ -sum_{i=1}^{n}frac{partial }{partial x_i}mathcal{A}_i(x,u(x), abla u(x))+mathcal{B}(x,u(x),abla u(x))=0.
Azeddine Baalal, Nedra Belhaj Rhouma
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Liouville's type results for singular anisotropic operators
Analysis and Geometry in Metric SpacesWe present two Liouville-type results for solutions to anisotropic elliptic equations that have a growth of power 2 along the first ss coordinate directions and of power pp, with ...
Maria Cassanello Filippo +2 more
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Global and blow up solutions to cross diffusion systems
Advances in Nonlinear Analysis, 2015 Necessary and sufficient conditions for global existence of classical solutions to a class of cross diffusion systems on n-dimensional domains are given. Examples of blow up solutions are also presented.
Ahmad Shair, Le Dung
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On the instability for the cubic nonlinear Schrodinger equation
, 2007 We study the flow map associated to the cubic Schrodinger equation in space dimension at least three.
Burq +5 more
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Global smooth solution to the n-dimensional liquid crystal equations with fractional dissipation
Demonstratio MathematicaIn this article, we focus on the global regularity of n-dimensional liquid crystal equations with fractional dissipation terms (−Δ)αu{\left(-\Delta )}^{\alpha }u and (−Δ)βd{\left(-\Delta )}^{\beta }d.
Li Wei, Wu Qiongru
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