# Asymptotic behavior of global solutions of the $u_t=\Delta u + u^{p}$

@inproceedings{Barraza2008AsymptoticBO, title={Asymptotic behavior of global solutions of the \$u_t=\Delta u + u^\{p\}\$}, author={Oscar A. Barraza and Laura B. Langoni}, year={2008} }

- Published 2008

We study the asymptotic behavior of nonnegative solutions of the semilinear parabolic problem
{u_t=\Delta u + u^{p}, x\in\mathbb{R}^{N}, t>0
u(0)=u_{0}, x\in\mathbb{R}^{N}, t=0.
It is known that the nonnegative solution $u(t)$ of this problem blows up in finite time for $1 1+ 2/N$ and the norm of $u_{0}$ is small enough, the problem admits global solution. In this work, we use the entropy method to obtain the decay rate of the global solution $u(t)$.

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 13 REFERENCES

## On the Cauchy Problem for Reaction-Diffusion Equations

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## Asymptotic behavior of solutions of a semilinear heat equation with subcritical nonlinearity

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Remarks on the large time behaviour of a nonlinear diffusion equation

VIEW 5 EXCERPTS

HIGHLY INFLUENTIAL

## On the Blow up Problem for Semilinear Heat Equations

VIEW 1 EXCERPT

## J

VIEW 1 EXCERPT

## J

VIEW 1 EXCERPT