## Tokyo Journal of Mathematics

### Time-Space Estimates of Solutions to General Semilinear Parabolic Equations

Changxing MIAO

#### Abstract

We study the Cauchy problem and the initial boundary value problem (IBVP) for nonlinear parabolic equations in $\mathcal{C}_b([0,T);L^p)$ and $L^q(0,T;L^p)$. We give a unified method to construct local mild solutions of the Cauchy problem or IBVP for a class of nonlinear parabolic equations in $\mathcal{C}_b([0,T);L^p)$ or $L^q(0,T;L^p)$ by introducing admissible triplet, generalized admissible triplet and establishing time space estimates for the solutions to the linear parabolic equations. Moreover, using our method, we also obtain the existence of global small solutions to the nonlinear parabolic equations.

#### Article information

Source
Tokyo J. Math., Volume 24, Number 1 (2001), 245-276.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1255958327

Digital Object Identifier
doi:10.3836/tjm/1255958327

Mathematical Reviews number (MathSciNet)
MR1844433

Zentralblatt MATH identifier
1106.35027

#### Citation

MIAO, Changxing. Time-Space Estimates of Solutions to General Semilinear Parabolic Equations. Tokyo J. Math. 24 (2001), no. 1, 245--276. doi:10.3836/tjm/1255958327. https://projecteuclid.org/euclid.tjm/1255958327