A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral I | Zendy

Lothar von Wolfersdorf | Zendy

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A Class of Partial Integro-Differential Equations with Correlation-Convolution Integral I

Author(s) -

Lothar von Wolfersdorf

Publication year - 2004

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1185

Subject(s) - mathematics , uniqueness , convolution (computer science) , integral equation , mathematical analysis , class (philosophy) , quadratic equation , rectangle , nonlinear system , integro differential equation , lebesgue integration , differential equation , first order partial differential equation , geometry , physics , quantum mechanics , machine learning , artificial intelligence , artificial neural network , computer science

By means of the iteration method with weighted norms existence and uniqueness theorems are proved for three classes of nonlinear integral equations and first order integro-differential equations in two variables. The quadratic nonlinearity is given by the correlation-convolution integral. Existence and uniqueness of the solutions are shown in Lebesgue spaces with mixed norms in rectangle and strip.

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