Noriko Mizoguchi

Diffusion-Induced Blowup in a Nonlinear Parabolic System

A two-component semilinear parabolic system on a bounded domain with Neumann boundary conditions is studied. It is shown that for a certain kind of nonlinearity, the blowup of solutions may occur when the diffusion coefficients are not equal, though the corresponding ODE possesses a globally stable equilibrium.

Blowup and life span of solutions for a semilinear parabolic equation

This paper is concerned with the Cauchy problem \[ \left \{ \begin{array}{ll} u _t = \Delta u + |u| ^{ p-1 } u & \quad \mbox{ in } \mathbf{R}^N \times (0, \infty), \\ u (x,0) = u_0(x) & \quad \mbox{ in } \mathbf{R}^N, \end{array} \right. \] where

Blow-up rate of type II and the braid group theory

p > 1

Blowup rate of solutions for a semilinear heat equation with the Neumann boundary condition

. Let

Existence of periodic solutions for equations of evolving curves

\Omega

Generation of infinitely many solutions of semilinear elliptic equation in two dimensional annulus

be a set in

Slow decay of solutions in a semilinear dissipative parabolic equation

\mathbf{R}^N

Critical exponents for the blow-up of solutions with sign changes in a semilinear parabolic equation

given by \[ \Omega \equiv \left\{ (r,\omega) \in \mathbf{R}^+ \times S^{N-1} \ : \ r > R, \ d ( \omega,\omega_0 ) 0

Rate of Type II blowup for a semilinear heat equation

,

On the behavior of solutions for a semilinear parabolic equation with supercritical nonlinearity

c > 0