Blow-up of Solutions of Nonlinear Parabolic Inequalities
نویسنده
چکیده
We study nonnegative solutions u(x, t) of the nonlinear parabolic inequalities au ≤ ut −∆u ≤ u in various subsets of R×R, where λ > n+2 n and a ∈ (0, 1) are constants. We show that changing the value of a in the open interval (0, 1) can dramatically affect the blow-up of these solutions.
منابع مشابه
A 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 کاملBlow-up of Solutions to Parabolic Inequalities in the Heisenberg Group
We establish a Fujita-type theorem for the blow-up of nonnegative solutions to a certain class of parabolic inequalities in the Heisenberg group. Our proof is based on a duality argument.
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 کاملBlow-Up Phenomena for a Class of Parabolic Systems with Time Dependent Coefficients
Blow-up phenomena for solutions of some nonlinear parabolic systems with time dependent coefficients are investigated. Both lower and upper bounds for the blow-up time are derived when blow-up occurs.
متن کاملLiouville Theorems, a Priori Estimates, and Blow-up Rates for Solutions of Indefinite Superlinear Parabolic Problems
In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.
متن کامل