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b s t r a c t In this paper, we consider the differential-operator equation du(t) dt +Au(t) =0, with Aaself-adjoint unboundedoperator coefficient, which does not have afixed sign.In this work, we will use a modified quasi-boundary value method; we obtain an approximate non-local problem depending on a small parameter ??]0,1[.(C)2013Else
b s t r a c t In this paper, we consider the differential-operator equation du(t) dt +Au(t) =0, with Aaself-adjoint unboundedoperator coefficient, which does not have afixed sign. The Cauchy problem for the equation above with conditions of the form u(0) = f or u(T) =f, is known to be an ill-posed problem. In this work, we will use a modified quasi-boundary value method; we obtain an approximate non-local problem depending on a small parameter α ∈ ]0,1[. We show that the approximate problems are well-posed and that their solutions converge if the original problem has a classical solution. We also obtain a convergence result for these solutions. ©2013Else
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