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- Title
Global and Blow-Up Solutions for a Class of Nonlinear Parabolic Problems under Robin Boundary Condition.
- Authors
Lingling Zhang; Hui Wang
- Abstract
We discuss the global and blow-up solutions of the following nonlinear parabolic problems with a gradient term under Robin boundary conditions: (b(u))t = Δ ⋅ (h(t)k(x)a(u)Δu) + f(x,u,¦Δu¦²,t), in D x (0,T), (∂u/∂n) + yu = 0, on ∂D x (0,T), u(x,0) = u0(x) > 0, in ..., where D ⊂ RN (N ≥ 2) is a bounded domain with smooth boundary ∂D. Under some appropriate assumption on the functions f, h, k, b, and a and initial value u0, we obtain 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." Our approach depends heavily on the maximum principles.
- Subjects
NONLINEAR equations; PARABOLIC differential equations; GRADIENT-index devices; HOROLOGY; NUMERICAL solutions to equations
- Publication
Abstract & Applied Analysis, 2014, p1
- ISSN
1085-3375
- Publication type
Article
- DOI
10.1155/2014/241650