Displaying similar documents to “Solutions of a linear second order equation of parabolic type defined in an unbounded domain”

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. ...

On the Cauchy problem for a class of parabolic equations with variable density

Shoshana Kamin, Robert Kersner, Alberto Tesei (1998)

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

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The well-posedness of the Cauchy problem for a class of parabolic equations with variable density is investigated. Necessary and sufficient conditions for existence and uniqueness in the class of bounded solutions are proved. If these conditions fail, sufficient conditions are given to ensure well-posedness in the class of bounded solutions which satisfy suitable constraints at infinity.