45K05 Integro-partial differential equations

Overview

This topic studies integro-partial differential equations in the setting of integro-partial differential equations, with emphasis on foundational results, operator behavior, and analytic applications.

Related Wikipedia Page

Integrodifferential equation (Wikipedia)

Useful Links

• Integrodifferential equation (Wikipedia)
• Partial differential equation (Wikipedia)
• Boundary value problem (Wikipedia)

Key Ideas

• Structural properties of the underlying analytic objects
• Continuity, boundedness, and convergence principles
• Interaction between abstract theory and computational/application contexts

Typical Uses

Used in research and advanced applications involving integro-partial differential equations, including representation, solvability, and stability analysis.

Applications

• Functional and harmonic analysis
• Operator and algebraic methods
• Mathematical physics and PDE models

References

• Ladyzhenskaya, O. A. (1985). The Boundary Value Problems of Mathematical Physics. New York: Springer.
• Polyanin, A. D. and Manzhirov, A. V. (2008). Handbook of Integral Equations. 2nd edn. Boca Raton, FL: CRC Press.
• Recent journal-paper search for Integro-partial differential equations
• Google Scholar (PDF results): Ladyzhenskaya, O. A. (1985). The Boundary Value Problems of Mathematical Physics. New York: Springer.

Recommended Textbooks

• Ladyzhenskaya, O. A. (1985). The Boundary Value Problems of Mathematical Physics. New York: Springer. — Amazon · Bookshop.org
• Polyanin, A. D. and Manzhirov, A. V. (2008). Handbook of Integral Equations. 2nd edn. Boca Raton, FL: CRC Press. — Amazon · Bookshop.org