Global and blow-up solutions for nonlinear parabolic problems with a gradient term under Robin boundary conditions
نویسنده
چکیده
where D⊂RN (N≥ 2) is a bounded domain with smooth boundary ∂D. By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of a global solution, an upper estimate of the global solution, the sufficient conditions for the existence of a blow-up solution, an upper bound for ‘blow-up time’, and an upper estimate of ‘blow-up rate’ are specified under some appropriate assumptions on the functions f , g, b and initial value u0. MSC: 35K55; 35B05; 35K57
منابع مشابه
Global 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 کاملThe Fujita phenomenon in exterior domains under the Robin boundary conditions
The Fujita phenomenon for nonlinear parabolic problems ∂tu = ∆u+ u p in an exterior domain of R under the Robin boundary conditions is investigated in the superlinear case. As in the case of Dirichlet boundary conditions (see Trans. Amer. Math. Soc 316 (1989), 595-622 and Isr. J. Math. 98 (1997), 141-156), it turns out that there exists a critical exponent p = 1+2/N such that blow-up of positiv...
متن کاملBlow-up phenomena for a class of quasilinear parabolic problems under Robin boundary condition
This paper deals with a class of heat emission processes in a medium with a nonegative source, a nonlinear decreasing thermal conductivity and a linear radiation (Robin) boundary condition. For such heat emission problems, using a differential inequality technique, we establish conditions on the data sufficient to guarantee that the blow-up of the solutions does occur or does not occur. In addi...
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 کامل