Wellposedness of hyperbolic evolution equations in Banach spaces

This paper is withdrawn because of an error in Lemma 3.1

This paper has been withdrawn by the author due to a crucial mistakes.

This paper has been withdrawn, and is replaced with paper "Solvability of elliptic systems with square integrable boundary data" by the same authors.

Known investigations of nonlinear evolution equations $${dx\over dt} + A(t)x(t) = f(t)\ ,\quad x(t_{0}) = x^{0},\ \quad t_{0} \le t < \infty\ , \eqno(0.1)$$ with monotone operators $A(t)$ acting from reflexive Banach space $B$ to dual space $B^*$, usually assume that along with $B$ and $B^*$ there is a Hilbert space $H$ and continuous imbedding $B \hookrightarrow H$ in the triplet $$B \hookrightarrow H \hookrightarrow B^*\ ; \eqno(0.2)$$ and that $B$ is dense in $H$. ...

The paper has been withdrawn by the author due to a gap in Proof of Theorem 1.1.

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In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The framework of our abstract result includes, for example, finite dimensional ordinary differential equations (ODEs), semilinear deterministic partial differential equations (PDEs), as well as certain additive noise driven stochastic partial differential equations (SPDEs) as special cases. The framework of ...

This paper has been withdrawn by the author, since the author does not have enough time to answer every questions on this result.

This paper has been withdrawn by the author due to an error estimate in Lemma 3.1.

This paper is being withdrawn by the author due a serious flaw.