共查询到20条相似文献,搜索用时 562 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.
The Nonexistence of the Solutions for the Non-Newtonian Filtration Equation with Absorption 下载免费PDF全文
Qitong Ou 《偏微分方程(英文版)》2021,34(4):369-378
The paper proves the nonexistence of the solution for the following Cauchy problem\begin{align*}\begin{cases}u_{t} ={\rm div}\left(\left|\nabla u^{m} \right|^{p-2} \nabla u^{m} \right)-\lambda \; u^{q},&\qquad \left(x,t\right)\in S_{T} ={\mathbb{R}}^N \times \left(0,T\right), \\u\left(x,\; 0\right)=\delta \left(x\right), &\qquad x\in {\mathbb{R}}^,\end{cases}\end{align*}under some conditions on \textit{m,p,q},$\lambda$, where $\delta $ is Dirac function. 相似文献
3.
Marcelo M. Cavalcanti Valéria N. Domingos Cavalcanti Ryuichi Fukuoka Daniel Toundykov 《Journal of Evolution Equations》2009,9(1):143-169
This paper is devoted to the study of uniform energy decay rates of solutions to the wave equation with Cauchy–Ventcel boundary
conditions:
4.
Daomin Cao Shusen Yan 《Calculus of Variations and Partial Differential Equations》2010,38(3-4):471-501
In this paper, we will prove the existence of infinitely many solutions for the following elliptic problem with critical Sobolev growth and a Hardy potential: $$-\Delta u-\frac{\mu}{|x|^2}u = |u|^{2^{\ast}-2}u+a u\quad {\rm in}\;\Omega,\quad u=0 \quad {\rm on}\; \partial\Omega,\qquad (*)$$ under the assumptions that N ≥ 7, ${\mu\in \left[0,\frac{(N-2)^2}4-4\right)}$ and a > 0, where ${2^{\ast}=\frac{2N}{N-2}}$ , and Ω is an open bounded domain in ${\mathbb{R}^N}$ which contains the origin. To achieve this goal, we consider the following perturbed problem of (*), which is of subcritical growth, $$-\Delta u-\frac{\mu}{|x|^2}u = |u|^{2^{\ast}-2-\varepsilon_n}u+au \quad {\rm in}\,\Omega, \quad u=0 \quad {\rm on}\;\partial\Omega,\qquad(\ast\ast)_n$$ where ${\varepsilon_{n} > 0}$ is small and ${\varepsilon_n \to 0}$ as n → + ∞. By the critical point theory for the even functionals, for each fixed ${\varepsilon_{n} > 0}$ small, (**) n has a sequence of solutions ${u_{k,\varepsilon_{n}} \in H^{1}_{0}(\Omega)}$ . We obtain the existence of infinitely many solutions for (*) by showing that as n → ∞, ${u_{k,\varepsilon_{n}}}$ converges strongly in ${H^{1}_{0}(\Omega)}$ to u k , which must be a solution of (*). Such a convergence is obtained by applying a local Pohozaev identity to exclude the possibility of the concentration of ${\{u_{k,\varepsilon_n}\}}$ . 相似文献
5.
Lucio Boccardo 《Milan Journal of Mathematics》2011,79(1):193-206
The aim of this work is to study the existence of solutions of quasilinear elliptic problems of the type
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