On blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions
نویسنده
چکیده
We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as t→ ∞. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.
منابع مشابه
On homogenization problems for fully nonlinear equations with oscillating Dirichlet boundary conditions
We study two types of asymptotic problems whose common feature and difficultyis to exhibit oscillating Dirichlet boundary conditions : the main contribution of this article is to show how to recover the Dirichlet boundary condition for the limiting equation. These two types of problems are (i) periodic homogenization problems for fully nonlinear, second-order elliptic partial differential equat...
متن کاملBlow up problems for a degenerate parabolic equation with nonlocal source and nonlocal nonlinear boundary condition
* Correspondence: zhgs917@163. com Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and globa...
متن کاملBlow-up in the Parablic Problems under Nonlinear Boundary Conditions
The paper deals with a degenerate and singular parabolic equation with nonlinear boundary condition. We first get the behavior of the solution at infinity, and establish the critical global existence exponent and critical Fujita exponent for the fast diffusive equation, furthermore give the blow-up set and upper bound of the blow-up rate for the nonglobal solutions.
متن کاملGlobal and blow-up solutions for quasilinear parabolic equations with a gradient term and nonlinear boundary flux
This work is concerned with positive classical solutions for a quasilinear parabolic equation with a gradient term and nonlinear boundary flux. We find sufficient conditions for the existence of global and blow-up solutions. Moreover, an upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’ and an upper estimate of the global solution are given. Finally, some application e...
متن کاملA note on critical point and blow-up rates for singular and degenerate parabolic equations
In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...
متن کامل