Improperly posed Cauchy problems are the primary topics in this discussion which assumes that the geometry and coefficients of the equations are known precisely. Appropriate references are made to other classes of improperly posed problems. The contents include straight forward examples of methods eigenfunction, quasireversibility, logarithmic convexity, Lagrange identity, and weighted energy used in treating improperly posed Cauchy problems. The Cauchy problem for a class of second order operator equations is examined as is the question of determining explicit stability inequalities for solving the Cauchy problem for elliptic equations. Among other things, an example with improperly posed perturbed and unperturbed problems is discussed and concavity methods are used to investigate finite escape time for classes of operator equations.
Author(s): L. E. Payne
Series: CBMS-NSF Regional Conference Series in Applied Mathematics
Edition: SIAM
Publisher: Society for Industrial Mathematics
Year: 1987
Language: English
Pages: 84
Improperly Posed Problems in Partial Differential Equations......Page 1
Contents......Page 5
Preface......Page 7
Improperly Posed Problems in Partial Differential Equations......Page 9
Methods and examples.......Page 14
Second order operator equations.......Page 27
Remarks on continuous dependence on boundary data, coefficients, geometry,and values of the operator.......Page 32
The Cauchy problem for elliptic equations.......Page 38
Singular perturbations in improperly posed problems.......Page 43
Nonexistence and growth of solutions of Schrodinger-type equations.......Page 50
Finite escape time; concavity methods.......Page 52
Finite escape time; other methods.......Page 59
Miscellaneous results.......Page 64
Bibliography......Page 70
