Inverse Problems · 1994 · 12 citations · 3 references
Natural SciencesMathematicsDifferential EquationsBoundary ConditionsBoundary-value ProblemsInitial ConditionsInitial Value ProblemsInverse ProblemsPartial Differential EquationsBoundary Condition IdentificationGlobal Existence TheoryInitial Boundary ConditionsInitial-boundary Value ProblemsInverse Boundary-value ProblemsLocal Existence TheoryParabolic Boundary-value ProblemsParabolic Partial Differential Equations
We are concerned with the parabolic inverse problem of finding (u(x,t), b(t)) satisfying the equation ut=uxx+b(t)ux x in (0,1), t>0 subject to some initial-boundary conditions and an overspecified datum on b(t). Some local existence and global existence theorems are proved and a non-existence result for a global solution is given.
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