REGULARITY FOR SOLUTIONS OF FIRST ORDER EVOLUTION EQUATIONS OF VOLTERRA TYPE
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In this paper we study the semilinear first order evolution problems of Volterra type with Lipschitz continuous nonlinearities. Using the variational formulation of problems due to Dautray and Lions [\ref{D-L}], we have proved the fundamental results on existence, uniqueness and continuous dependence of solutions. Especially in the proof of the regularity we have used the double regularization method. Applications to nonlinear partial integro-differential equations are given.
Abstract
In this paper we study the semilinear first order evolution problems of Volterra type with Lipschitz continuous nonlinearities. Using the variational formulation of problems due to Dautray and Lions [\ref{D-L}], we have proved the fundamental results on existence, uniqueness and continuous dependence of solutions. Especially in the proof of the regularity we have used the double regularization method. Applications to nonlinear partial integro-differential equations are given.
참고문헌 (13)
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