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Displaying similar documents to “Existence and uniqueness of solutions Cauchy problem for nonlinear infinite systems of parabolic differential-functional equations.”

Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations

Stanisław Brzychczy (1999)

Annales Polonici Mathematici

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We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.

L -estimates for solutions of nonlinear parabolic systems with gradient linear growth

Wojciech Zajączkowski (1996)

Banach Center Publications

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Existence of weak solutions and an L -estimate are shown for nonlinear nondegenerate parabolic systems with linear growth conditions with respect to the gradient. The L -estimate is proved for equations with coefficients continuous with respect to x and t in the general main part, and for diagonal systems with coefficients satisfying the Carathéodory condition.