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.

MSC:

 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)
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References:

 [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
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