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Some Closed‐Form Solutions of Burgers’ Equation
Author(s) -
McAsey M.,
Rubel L. A.
Publication year - 1993
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1993883173
Subject(s) - burgers' equation , mathematics , mathematical analysis , function (biology) , constant (computer programming) , variable (mathematics) , similarity solution , partial differential equation , physics , thermodynamics , computer science , boundary layer , evolutionary biology , biology , programming language
This paper shows how to use the method of quasisolutions to construct exact solutions to Burgers’ equation. A function υ=υ ( x, y ) is called a quasisolution of a PDE in case there exists a function φ (not a constant function) of one variable so that u ( x, y )= φ ( υ ( x, y )) is a solution of the equation. We prove a theorem giving necessary and sufficient conditions for υ to be a quasisolution to Burgers’ equation. A function φ can then be found explicitly so that u=φ ( υ ) is an actual solution. Combining this technique with similarity methods, we find a continuum of solutions to Burgers' equation.