Displaying similar documents to “Time averaging for random nonlinear abstract parabolic equations.”

Characterization of the interior regularity for parabolic systems with discontinuous coefficients

Dian K. Palagachev, Lubomira G. Softova (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We deal in this Note with linear parabolic (in sense of Petrovskij) systems of order 2 b with discontinuous principal coefficients belonging to V M O L . By means of a priori estimates in Sobolev-Morrey spaces we give a precise characterization of the Morrey, BMO and Hölder regularity of the solutions and their derivatives up to order 2 b - 1 .

Existence of solutions for infinite systems of parabolic equations with functional dependence

Anna Pudełko (2005)

Annales Polonici Mathematici

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The Cauchy problem for an infinite system of parabolic type equations is studied. General operators of parabolic type of second order with variable coefficients are considered and the system is weakly coupled. We prove the existence and uniqueness of a bounded solution under Carathéodory type conditions and its differentiability, as well as the existence and uniqueness in the class of functions satisfying a natural growth condition. Both results are obtained by the fixed point method. ...