Finite Time Blow-up and Global Solutions for Semilinear Parabolic Equations with Initial Data at High Energy Level

نویسندگان

  • Filippo Gazzola
  • Tobias Weth
  • Takashi Suzuki
چکیده

For a class of semilinear parabolic equations on a bounded domain Ω, we analyze the behavior of the solutions when the initial data varies in the phase space H 0 (Ω). We obtain both global solutions and finite time blow-up solutions. Our main tools are the comparison principle and variational methods. Particular attention is paid to initial data at high energy level; to this end, a basic new idea is to exploit the weak dissipativity (respectively antidissipativity) of the semiflow inside (respectively outside) the Nehari manifold.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Finite-time Blow-up and Global Solutions for Some Nonlinear Parabolic Equations

For a class of semilinear parabolic equations, we prove both global existence and finite-time blow-up depending on the initial datum. The proofs involve tools from the potential-well theory, from the criticalpoint theory, and from classical comparison principles.

متن کامل

Global Existence, Exponential Decay and Finite Time Blow-up of Solutions for a Class of Semilinear Pseudo-parabolic Equations with Conical Degeneration

In this paper, we study the semilinear pseudo-parabolic equations ut − 4Bu − 4But = |u|p−1 u on a manifold with conical singularity, where 4B is Fuchsian type Laplace operator investigated with totally characteristic degeneracy on the boundary x1 = 0. Firstly, we discuss the invariant sets and the vacuum isolating behavior of solutions with the help of a family of potential wells. Then, we deri...

متن کامل

Blow-up at the Boundary for Degenerate Semilinear Parabolic Equations

This paper concerns a superlinear parabolic equation, degenerate in the time derivative. It is shown that the solution may blow up in finite time. Moreover it is proved that for a large class of initial data blow-up occurs at the boundary of the domain when the nonlinearity is no worse than quadratic. Various estimates are obtained which determine the asymptotic behaviour near the blow-up. The ...

متن کامل

Global existence versus blow up for some models of interacting particles Piotr

We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst–Planck and the Debye–Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and o...

متن کامل

Global existence versus blow up for some models of interacting particles

We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst–Planck and the Debye–Hückel drift-diffusion systems as well as parabolic-elliptic systems of chemotaxis. In the case of a model of self-gravitating particles, we also give a result on the finite time blow up of solutions with localized and o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004