35Cxx Representations of solutions
This subtopic studies representations of solutions to PDEs, including integral formulas, Green function methods, and transform techniques.
Specific topics
35C05 Solutions to PDEs in closed form
Overview
35C05 studies solutions to pdes in closed form in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for solutions to pdes in closed form
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C06 Self-similar solutions to PDEs
Overview
35C06 studies self-similar solutions to pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for self-similar solutions to pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C07 Traveling wave solutions of PDEs
Overview
35C07 studies traveling wave solutions of pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for traveling wave solutions of pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C08 Soliton solutions of PDEs
Overview
35C08 studies soliton solutions of pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for soliton solutions of pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C09 Trigonometric solutions to PDEs
Overview
35C09 studies trigonometric solutions to pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for trigonometric solutions to pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C10 Series solutions to PDEs
Overview
35C10 studies series solutions to pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for series solutions to pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C11 Polynomial solutions to PDEs
Overview
35C11 studies polynomial solutions to pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for polynomial solutions to pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C15 Integral representations of solutions to PDEs
Overview
35C15 studies integral representations of solutions to pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for integral representations of solutions to pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks
35C20 Asymptotic expansions of solutions to PDEs
Overview
35C20 studies asymptotic expansions of solutions to pdes in representations of solutions. It studies explicit or integral representations of PDE solutions, including Green functions, kernels, and transforms.
Related Wikipedia Page
Representations Of Solutions (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for asymptotic expansions of solutions to pdes
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used to solve boundary-value and initial-value problems through representation formulas.
Applications
- Green function methods
- Kernel representations
- Integral transforms
References
Recommended Textbooks