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Global existence of solutions of semilinear parabolic evolution equations. (English) Zbl 1038.35025

The authors deal with the problem of the existence of a global solution to the following semilinear problem \[ \partial_tu+ Au=F(u),\;u(0)= u_0\tag{1} \] where \(A\) is the infinitesimal generator of a \(C_0\)-semigroup \(\{S(t)\}_{t\geq 0}\) on \(V\) and the nonlinear mapping \(F\) acts continuously from \(E\) into \(V\). Here \(E\) and \(V\) are \(B\)-spaces such that \(E\) is densely and continuously embedded into \(V\). They apply their abstract results to the heat equation with first order nonlinear perturbations, Cahn-Hilliard and Fitz Hugh-Nagumo systems.

MSC:

35K55 Nonlinear parabolic equations
35K15 Initial value problems for second-order parabolic equations
35K90 Abstract parabolic equations
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