Premium
Solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $$\end{document} . Exact solutions of some partial differential equations in mechanics and physics
Author(s) -
AbdelGawad H. I.
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140903
Subject(s) - mathematics , partial differential equation , first order partial differential equation , mathematical physics , operator (biology) , differential equation , commutative property , mathematical analysis , pure mathematics , chemistry , biochemistry , repressor , transcription factor , gene
The solutions of the equation \documentclass{article}\pagestyle{empty}\begin{document}$ \partial _t^n f(x,t) = \hat L(x,t)f(x,t) + S(x,t) $\end{document} , for L̂ a linear operator are derived. Different forms for L̂ whether it is time independent or time dependent and self‐commutative (or not) at different times are considered separately. By using the results obtained, exact solutions of some partial differential equations are found for the first time.