A Degenerate Nonlinear Cauchy Problem

Document Type

Article

Publication Date

1-1-1982

Abstract

Many initial boundary value problems can be put in the form: d/dt(B(t)u(t)) + A(t, u(t)) =f(t) where A:LP(0, T, V)→LP (0, T, V’) is either a pseudo monotone or Type M operator, and V is a reflexive Banach space. B(t) is a linear continuous mapping of V to V’ which may vanish. Conditions are given on the operators B(t) and A(t, ·) that insure the existence of a solution to the Cauchy problem. Also, the exact meaning of what is meant by an initial condition to such an equation is made precise, and the collection of possible initial values is characterized as being the domain of the square root of a certain operator. These results generalize earlier results in which the operators B(t) do not depend on t. © 1982, Taylor & Francis Group, LLC. All rights reserved.

Publication Title

Applicable Analysis

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