Existence and uniqueness of a solution to the Dirichlet problem for a quasilinear equation inside and outside a paraboloid

We consider the Dirichlet problem for the equation

Highly time-oscillating solutions for very fast diffusion equations

This work is concerned with the fast diffusion equation

Singular limits for 2-dimensional elliptic problem involving exponential nonlinearity with nonlinear gradient term

Given a bounded open regular set W ì \mathbbR²{\Omega \subset \mathbb{R}^2} and x₁, x₂, ?, x_m ? W{x_1, x_2, \ldots, x_m \in \Omega}, we give a sufficient condition for the problem

On the global well-posedness of a class of Boussinesq�CNavier�CStokes systems

In this paper we consider the following 2D Boussinesq–Navier–Stokes systems

Quasilinear elliptic equations on \mathbbRN{\mathbb{R}^{N}} with singular potentials and bounded nonlinearity

We study the existence and multiplicity of nontrivial radial solutions of the quasilinear equation

Two-dimensional variational problems with a wide range of anisotropy

We consider local minimizers u:\mathbbR² é W? \mathbbR^M u:{\mathbb{R}^2} \supset \Omega \to {\mathbb{R}^M} of the variational integral

Gradient estimates for the elliptic and parabolic Lichnerowicz equations on compact manifolds

Let (M, g) be a smooth compact Riemannian manifold of dimension n ≥ 3. Denote D_g=-div_g?{\Delta_g=-{\rm div}_g\nabla} the Laplace–Beltrami operator. We establish some local gradient estimates for the positive solutions of the Lichnerowicz equation

Multiple solutions to a nonlinear Schrödinger equation with Aharonov–Bohm magnetic potential

We consider the magnetic nonlinear Schrödinger equations $\begin{array}{ll}{\left(-i\nabla + sA\right)^{2} u + u \, = \, |u|^{p-2}\, u, \quad p \in (2, 6),} \\ \quad \quad {\left(-i\nabla + sA\right) ^{2}u \, = \, |u|^{4}\, u,}\end{array}$ in ${\Omega=\mathcal{O}\times \mathbb{R}}We consider the magnetic nonlinear Schr?dinger equations

ll(-i?+ sA)2 u + u   =  |u|p-2 u,     p ? (2, 6),         (-i?+ sA) 2u   =  |u|4 u,\begin{array}{ll}{\left(-i\nabla + sA\right)^{2} u + u \, = \, |u|^{p-2}\, u, \quad p \in (2, 6),} \\ \quad \quad {\left(-i\nabla + sA\right) ^{2}u \, = \, |u|^{4}\, u,}\end{array}      9. Renormalized solution for Stefan type problems: existence and uniqueness      Noureddine Igbida  Karima Sbihi  Petra Wittbold 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(1):69-93 We consider a class of nonlinear degenerate problems of Stefan type: $u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$ where β is a maximal monotone graph in ${\mathbb{R}^2,}We consider a class of nonlinear degenerate problems of Stefan type: ut- Dw -?F(u,w) = g(·,u),  w ? b(u)u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)      10. A note on uniqueness of entropy solutions to degenerate parabolic equations in {\mathbb{R}^N}      Boris Andreianov  Mohamed Maliki 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(1):109-118 We study the Cauchy problem in \mathbbRN{\mathbb{R}^N} for the parabolic equation ut+div F(u)=Dj(u),u_t+{\rm div}\,F(u)=\Delta\varphi(u),      设为首页 | 免责声明 | 关于勤云 | 加入收藏 Copyright©北京勤云科技发展有限公司  京ICP备09084417号

Renormalized solution for Stefan type problems: existence and uniqueness

We consider a class of nonlinear degenerate problems of Stefan type: $u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$ where β is a maximal monotone graph in ${\mathbb{R}^2,}We consider a class of nonlinear degenerate problems of Stefan type:

ut- Dw -?F(u,w) = g(·,u),  w ? b(u)u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)      10. A note on uniqueness of entropy solutions to degenerate parabolic equations in {\mathbb{R}^N}      Boris Andreianov  Mohamed Maliki 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(1):109-118 We study the Cauchy problem in \mathbbRN{\mathbb{R}^N} for the parabolic equation ut+div F(u)=Dj(u),u_t+{\rm div}\,F(u)=\Delta\varphi(u),

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Copyright©北京勤云科技发展有限公司  京ICP备09084417号

A note on uniqueness of entropy solutions to degenerate parabolic equations in {\mathbb{R}^N}

We study the Cauchy problem in \mathbbR^N{\mathbb{R}^N} for the parabolic equation