We consider the equation (including various functional-differential equations of retarded type) z_x(x, y) = f(x, y, T^(1)(x, y, z), · · · , T^(r)(x, y, z), z_y(x, y)) on the strip I = [0, a]xR, where T^(j) (j = 1, 2, · · · , r) are Volterra type operators. Existence, uniqueness and continuous dependence of a smooth solution on I for the Cauchy problem of the above equation with initial value z = g on [-p_0, 0]xR are proved. A quantitative estimate on the domain strip of the solution is given.

Existence, uniqueness and continuous dependence for a hereditary nonlinear functional partial differential equation of the first order

BRANDI, Primo;CEPPITELLI, Rita
1986

Abstract

We consider the equation (including various functional-differential equations of retarded type) z_x(x, y) = f(x, y, T^(1)(x, y, z), · · · , T^(r)(x, y, z), z_y(x, y)) on the strip I = [0, a]xR, where T^(j) (j = 1, 2, · · · , r) are Volterra type operators. Existence, uniqueness and continuous dependence of a smooth solution on I for the Cauchy problem of the above equation with initial value z = g on [-p_0, 0]xR are proved. A quantitative estimate on the domain strip of the solution is given.
1986
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/914500
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