A group analysis approach for a nonlinear differential system arising in diffusion phenomena. (English) Zbl 0872.35004

The authors consider a class of systems of differential equations of the special form \[ u_t= h(u,v),\quad v_t= [g(v) v_x+ f(v)u_x]_x, \] which arises in diffusion phenomena (diffusion of a solvent into a polymer slab). Using equivalence transformations, they give a classification, then Lie symmetries and classes of exact solutions are computed in special cases.


35A22 Transform methods (e.g., integral transforms) applied to PDEs
35C05 Solutions to PDEs in closed form
35K57 Reaction-diffusion equations
35Q80 Applications of PDE in areas other than physics (MSC2000)
Full Text: DOI


[1] Akhatov I. Sh., Mod. Prob. Math. 34 pp 3– (1989)
[2] DOI: 10.1063/1.529042 · Zbl 0737.35099
[3] DOI: 10.1063/1.529841 · Zbl 0761.35104
[4] Torrisi M., Lie Groups Applic. 1 pp 1– (1994)
[5] DOI: 10.1137/0150077 · Zbl 0732.35040
[6] DOI: 10.1137/0151023 · Zbl 0718.76095
[7] DOI: 10.1006/jmaa.1994.1213 · Zbl 0809.35053
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.