Electron. J. Diff. Eqns., Vol. 2001(2001), No. 24, pp. 1-14.

Existence results for a class of semi-linear evolution equations

Eduardo Hernandez M.

Abstract:
We prove the existence of regular solutions for the quasi-linear evolution
$$ {d \over dt}(x(t)+g(t,x(t))=Ax(t)+f(t,x(t)), $$
where $A$ is the infinitesimal generator of an analytic semigroup of bounded linear operators defined on a Banach space and the functions $f, g$ are continuous.

Submitted December 14, 2000. Published April 10, 2001.
Math Subject Classifications: 35A05, 34G20, 34A09.
Key Words: Banach spaces, semigroup of linear operators, abstract differential equations, fractional powers of closed operators, regular solutions.

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Eduardo Hernandez M.
Departamento de Matematica
Instituto de Ciencias Matematicas de Sao Carlos
Universidade de Sao Paulo
Caixa Postal 668
13560-970 Sao Carlos, SP. Brazil
e-mail: lalohm@icmc.sc.usp.br

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