Open Access
June 2001 Time-Space Estimates of Solutions to General Semilinear Parabolic Equations
Changxing MIAO
Tokyo J. Math. 24(1): 245-276 (June 2001). DOI: 10.3836/tjm/1255958327


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.


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Changxing MIAO. "Time-Space Estimates of Solutions to General Semilinear Parabolic Equations." Tokyo J. Math. 24 (1) 245 - 276, June 2001.


Published: June 2001
First available in Project Euclid: 19 October 2009

zbMATH: 1106.35027
MathSciNet: MR1844433
Digital Object Identifier: 10.3836/tjm/1255958327

Rights: Copyright © 2001 Publication Committee for the Tokyo Journal of Mathematics

Vol.24 • No. 1 • June 2001
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