Blow-up in the Parablic Problems under Nonlinear Boundary Conditions
نویسنده
چکیده
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.
منابع مشابه
Blow-up in the Parabolic Problems under Nonlinear Boundary Conditions
In this paper, I consider nonlinear parabolic problems under nonlinear boundary conditions. I establish respectively the conditions on nonlinearities to guarantee that ( , ) u x t exists globally or blows up at some finite time. If blow-up occurs, an upper bound for the blow-up time is derived, under somewhat more restrictive conditions, lower bounds for the blow-up time are also derived.
متن کاملTransient behavior of solutions to a class of nonlinear boundary value problems
In this paper we consider the asymptotic behavior in time of solutions to the heat equation with certain nonlinear Neumann boundary conditions, ∂u/∂n = F (u). Here F is a function which grows superlinearly. In general solutions exist for only a finite time before “blowing up”, or they decay to zero as time approaches infinity. In both one and two space-dimensions we establish some conditions on...
متن کاملBLOW-UP AND NONGLOBAL SOLUTION FOR A FAMILY OF NONLINEAR HIGHER-ORDER EVOLUTION PROBLEM
In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...
متن کاملGlobal and blow-up solutions for nonlinear parabolic problems with a gradient term under Robin boundary conditions
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 unde...
متن کاملOn blow-up and asymptotic behavior of solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions
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.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- JNW
دوره 9 شماره
صفحات -
تاریخ انتشار 2014