On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unbounded coefficients.

Yehuda Pinchover

Displaying similar documents to “On uniqueness and nonuniqueness of the positive Cauchy problem for parabolic equations with unbounded coefficients.”

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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. ...