Uperieure S Ormale N Ecole Stability of Blow-up Proole for Equation of the Type Stability of Blow-up Proole for Equation of the Type
نویسندگان
چکیده
Stability of blow-up proole for equation of the type u t = u + juj p?1 u Abstract In this paper, we consider the following nonlinear equation u t = u + juj p?1 u u(:; 0) = u 0 ; (and various extensions of this equation, where the maximum principle do not apply). We rst describe precisely the behavior of a blow-up solution near blow-up time and point. We then show a stability result on this behavior .
منابع مشابه
Finite time blow up of solutions of the Kirchhoff-type equation with variable exponents
In this work, we investigate the following Kirchhoff-type equation with variable exponent nonlinearities u_{tt}-M(‖∇u‖²)△u+|u_{t}|^{p(x)-2}u_{t}=|u|^{q(x)-2}u. We proved the blow up of solutions in finite time by using modified energy functional method.
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
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 existence, stability results and compact invariant sets for a quasilinear nonlocal wave equation on $mathbb{R}^{N}$
We discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of Kirchhoff Type [ u_{tt}-phi (x)||nabla u(t)||^{2}Delta u+delta u_{t}=|u|^{a}u,, x in mathbb{R}^{N} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $N geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$ is a positive function lying in $L^{N/2}(mathb...
متن کاملUperieure S Ormale N Ecole Morrey-campanato Estimates for Helmholtz Equation Morrey-campanato Estimates for Helmholtz Equation Morrey-campanato Estimates for Helmholtz Equation
We derive uniform weighted L 2 and Morrey-Campanato type estimates for Helmholtz Equations in a medium with a variable index which is not necessarily constant at innnity. Our technique is based on a multiplier method with appropriate weights which generalize those of Morawetz for the wave equation. We also extend our method to the wave equation.
متن کامل