Local and global solutions of well-posed integrated Cauchy problems

Pedro J. Miana¹

¹ Departamento de Matemáticas Instituto Universitario de Matemáticas y Aplicaciones Universidad de Zaragoza 50009 Zaragoza, Spain

Studia Mathematica, Tome 187 (2008) no. 3, pp. 219-232

Résumé

We study the local well-posed integrated Cauchy problem $$ v'(t)=Av(t)+{t^{\alpha }\over {\mit\Gamma} (\alpha+1 )} \, x,\ \quad v(0)=0, \ \quad t\in [0, \kappa), $$ with $\kappa>0$, $\alpha \ge 0$, and $x\in X$, where $X$ is a Banach space and $A$ a closed operator on $X$. We extend solutions increasing the regularity in $\alpha $. The global case $(\kappa=\infty)$ is also treated in detail. Growth of solutions is given in both cases.

Détail

DOI : 10.4064/sm187-3-2

Keywords: study local well posed integrated cauchy problem alpha mit gamma alpha quad quad kappa kappa alpha where banach space closed operator nbsp extend solutions increasing regularity alpha global kappa infty treated detail growth solutions given cases