共查询到20条相似文献,搜索用时 328 毫秒
1.
In this paper we prove existence and comparison results for nonlinear parabolic equations which are modeled on the problem
$\left\{{ll}{u_t - {\rm div}\,\left(\frac{1}{(1+|u|)^{\alpha}}|Du|^{p-2}Du\right)
=f\quad\hskip 2pt \,\,{\rm in}\,\Omega\times(0,T),}\\
{u=0\qquad\qquad\qquad\qquad\quad\quad\qquad{\rm
on}\,\partial\Omega\times(0,T),}\\
{u(x,0)=u_0(x)\quad\qquad\qquad\qquad\qquad{\rm
in}\,\Omega,}\right.$\left\{\begin{array}{ll}{u_t - {\rm div}\,\left(\frac{1}{(1+|u|)^{\alpha}}|Du|^{p-2}Du\right)
=f\quad\hskip 2pt \,\,{\rm in}\,\Omega\times(0,T),}\\
{u=0\qquad\qquad\qquad\qquad\quad\quad\qquad{\rm
on}\,\partial\Omega\times(0,T),}\\
{u(x,0)=u_0(x)\quad\qquad\qquad\qquad\qquad{\rm
in}\,\Omega,}\end{array}\right. 相似文献
2.
We study the existence of weak solutions for a nonlinear elliptic system of Lane-Emden type $$\left\{\begin{array}{ll} -\Delta u \; = \; {\rm sgn}(v)|v|^{p-1} & {\rm in}\;\mathbb{R}^N, \\ -\Delta v \; = \; -\rho(x){\rm sgn}(u)|u|^{\frac{1}{p-1}} + f(x, u) & {\rm in}\;\mathbb{R}^N, \\ u, v \to 0 \quad {\rm as} \quad |x| \to +\infty, \end{array}\right.$$ by means of the Mountain Pass Theorem and some compact imbeddings in weighted Sobolev spaces. 相似文献
3.
Patrick Winkert 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):289-302
In this paper we prove the L
∞-boundedness of solutions of the quasilinear elliptic equation
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