## Direchlet Boundary Value Problem

Direchlet Boundary Value Problem:

## Answers (4)

• In mathematics, the Dirichlet (or first-type) boundary condition is a type of boundary condition, named after Johann Peter Gustav Lejeune Dirichlet (1805–1859).[1] When imposed on an ordinary or a partial differential equation, it specifies the values a solution needs to take on the boundary of the domain. The question of finding solutions to such equations is known as the Dirichlet problem.
For an ordinary differential equation, for instance:

the Dirichlet boundary conditions on the interval take the form:

where and are given numbers.
For a partial differential equation, for instance:

where denotes the Laplacian, the Dirichlet boundary conditions on a domain take the form:

where f is a known function defined on the boundary .
Many other boundary conditions are possible. For example, there is the Cauchy boundary condition, or the mixed boundary condition which is a combination of the Dirichlet and Neumann
• www.boundaryvalueproblems.com/content/2010/1/325415
• In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional restraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions.
Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator.
To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed.
Among the earliest boundary value problems to be studied is the Dirichlet problem, of finding the harmonic functions (solutions to Laplace's equation); the solution was given by the Dirichlet's principle.
• please visit

www.boundaryvalueproblems.com/content/2010/1/325415

please rate me
Get homework help
More than 200 experts are waiting to help you now...
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://www.chegg.com/homework-help/questions-and-answers/direchlet-boundary-value-problem-q3560721", "fetch_time": 1369441453000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2013-20/segments/1368705300740/warc/CC-MAIN-20130516115500-00054-ip-10-60-113-184.ec2.internal.warc.gz", "warc_record_offset": 391952790, "warc_record_length": 8650, "token_count": 506, "char_count": 2549, "score": 3.765625, "int_score": 4, "crawl": "CC-MAIN-2013-20", "snapshot_type": "latest", "language": "en", "language_score": 0.9234505295753479, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00003-of-00064.parquet"}