Solutions of nonlinear SPDE via random Colombeau distribution
Çapar, Uluğ (2006) Solutions of nonlinear SPDE via random Colombeau distribution. [Working Paper / Technical Report] Sabanci University ID:SU_FENS_2006/0008
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The solutions of nonlinear SPDE are usually involved with the singular objects like the products of the Dirac delta, Heaviside functions and the nonlinear white-noise functionals which are diffucult to handle within the classical theory. In this work the framework is the white-noise space (Ω, ∑, V), where Ω in the space of tempered distributions, ∑ is an appropriate δ algebra and V is the Bochner -Minlos measure. Following  and a generalized s.p. is defined as measurable mapping Ω → GΩ(R n+1), where GΩ is the space of Colombeau distrubitions. In this set-up the solutions to the SPDE are sought in the representative platform using the represantatives in the Colembeau factor space, of the random excitations. When the moderateness of the represantative solutions are demonstrated, their equivalence classes constitute the Colombeau solutions. A shock-wave equation of the form U + U x U = W and a preypredator system with white-noise excitation are handled in this spirit. ( = denotes the association relation in the Colombeau theory).
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