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A method for reparameterizing mild solutions to nonlinear evolution equations. (English) Zbl 0694.35081
Existence of solutions of evolution differential equation \(u'(t)+A(t)u(t)\ni 0\), \(u(0)=x_ 0\) where \(A(t)\) is a multivalued m- accretive operator in a Banach space \(X\) is discussed in the case when a solution to \(v'(t)+B(t)v(t)\ni 0\), \(v(0)=x_ 0\) is known to exist and \(A\) and \(B\) are related by \(A(t)=r(t)B(t)\) with \(r(t)\) positive and integrable.
Reviewer: S.Tersian
MSC:
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
34G99 Differential equations in abstract spaces
35K55 Nonlinear parabolic equations
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References:
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