Composite Type Equations and Inverse Problems (Inverse and Iii-Posed Problems) 906764305X, 9789067643054
This monograph deals with the theory of well-posed boundary problems for general equations of composite type of the thir
129 55 781KB
English Pages 179 [181] Year 1999
Table of contents :
Chapter 1. Composite type equations as the original mathematical object
1.1. Equations of the composite type in mathematics and mathematical simulation
1.2. Canonical types of third order equations
1.3. Boundary-value problems for third order equations of composite type
1.3.1. Hyperbolic boundary-value problem. Uniqueness of regular solutions
1.3.2. Existence of the regularized solutions of the hyperbolic boundary-value problem
1.3.3. Existence of regular solutions of the hyperbolic boundary-value problem
1.3.4. The elliptic boundary-value problem. Uniqueness of regular solutions
1.3.5. Existence of generalized solutions of the elliptic boundary-value problem
1.3.6. Existence of regular solutions of the elliptic boundary-value problem
1.3.7. Correlation of the hyperbolic and elliptic boundary-value problems
1.3.8. Remark on the third order equations of the variable direction
1.3.9. Nonlocal problems for equations of composite type
Chapter 2. Solvability of inverse problems and other applications
2.1. Inverse problems for equations with partial derivatives
2.1.1. Linear inverse problems for elliptic and parabolic equations
2.1.2. On solvability of nonlinear inverse problems
2.2.Solvability of nonclassical boundary-value problems for equations of second order and third order
2.2.1. The mixed problem for second order equations not solved for the time derivative
2.2.2. Boundary-value problems for the second order equations of the mixed type
2.2.3. The problem with oblique derivative for equations of second and third orders
2.2.4. A problem of viscous elasticity and the third order equation in noncylindrical domains connected with this problem
Conclusion
Bibliography
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