On nonlinear diffusion equations with x-dependent convection and absorption

✍ Scribed by Changzheng Qu; P.G. Estévez

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 349 KB
• Volume: 57
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2004.02.027

✦ Synopsis

For the 1+1-dimensional nonlinear di usion equations with x-dependent convection and source terms ut = (D(u)ux)x + Q(x; u)ux + P(x; u), we obtain conditions under which the equations admit the second-order generalized conditional symmetries Á(x; u) = uxx + H (u)u 2

x + G(x; u)ux + F(x; u) and the ÿrst-order sign-invariants J (x; u) = ut -A(u)u 2

x -B(x; u)ux -C(x; u) on the solutions u(x; t). Several di erent generalized conditional symmetries and ÿrst-order sign-invariants for equations in which the di usion term o ers di erent possibilities (power-law, exponential, Mullin, Fujita) are presented. Exact solutions to the resulting equations corresponding to the generalized conditional symmetries and the ÿrst-order sign-invariants are constructed.