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Asymptotic behaviour of parabolic nonautonomous evolution equations
, 2002
"... The long term behaviour of autonomous linear Cauchy problems on a Banach space X has been studied systematically and quite successfully by means of spectral theory ..."
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Cited by 4 (1 self)
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The long term behaviour of autonomous linear Cauchy problems on a Banach space X has been studied systematically and quite successfully by means of spectral theory
WELLPOSEDNESS OF HYPERBOLIC EVOLUTION EQUATIONS IN BANACH SPACES
, 2005
"... Abstract. We study wellposedness of hyperbolic nonautonomous linear evolution equations u ′ (t) = A(t)u(t) in Banach spaces X. Using the theory of evolution semigroups, we develop two different notions of solvability, examine their properties and give existence and uniqueness theorems. At first we ..."
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Cited by 1 (1 self)
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Abstract. We study wellposedness of hyperbolic nonautonomous linear evolution equations u ′ (t) = A(t)u(t) in Banach spaces X. Using the theory of evolution semigroups, we develop two different notions of solvability, examine their properties and give existence and uniqueness theorems. At first we consider solutions which are limits of classical solutions. This concept is seen to coincide with weak solutions in our setting. Second, we study limits of solutions to suitable approximating problems. Here we obtain for separable Hilbert spaces X and skew adjoint operators A(t) an existence and uniqueness result under minimal additional assumptions. We apply our results to examples motivated from quantum theory. In particular, we show the existence of the time evolution in the theory of a massive bosonic quantum field with localized polynomial selfinteraction on two dimensional space time. 1.
L p –REGULARITY FOR PARABOLIC OPERATORS WITH UNBOUNDED TIME–DEPENDENT COEFFICIENTS
, 903
"... Abstract. We establish the maximal regularity for nonautonomous OrnsteinUhlenbeck operators in L pspaces with respect to a family of invariant measures, where p ∈ (1, +∞). This result follows from the maximal L pregularity for a class of elliptic operators with unbounded, timedependent drift coe ..."
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Abstract. We establish the maximal regularity for nonautonomous OrnsteinUhlenbeck operators in L pspaces with respect to a family of invariant measures, where p ∈ (1, +∞). This result follows from the maximal L pregularity for a class of elliptic operators with unbounded, timedependent drift coefficients and potentials acting on L p (R N) with Lebesgue measure. 1.
Vorsitzender des Promotionsausschusses:
, 2005
"... We establish the existence of Bogoliubov’s local scattering operators for P(ϕ)2 models of constructive quantum field theory in a nonperturbative way. To this end, we use the technique of evolution semigroups to prove a new result on wellposedness of the Cauchy problem for the timedependent Schrödin ..."
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We establish the existence of Bogoliubov’s local scattering operators for P(ϕ)2 models of constructive quantum field theory in a nonperturbative way. To this end, we use the technique of evolution semigroups to prove a new result on wellposedness of the Cauchy problem for the timedependent Schrödinger equation under very general assumptions.