Solutions for Multitime Reaction–Diffusion PDE

Cristian Ghiu and Constantin Udriste ()
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Cristian Ghiu: Department of Mathematical Methods and Models, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
Constantin Udriste: Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 19, 1-12

Abstract: A previous paper by our research group introduced the nonlinear multitime reaction–diffusion PDE (with oblique derivative) as a generalized version of the single-time model. This paper states and uses some hypotheses that allow the finding of some important explicit families of the exact solutions for multitime reaction–diffusion PDEs of any dimension that have a multitemporal directional derivative term. Some direct methods for determining the exact solutions of nonlinear PDEs from mathematical physics are presented. In the single-time case, our methods present many advantages in comparison with other known approaches. Particularly, we obtained classes of ODEs and classes of PDEs whose solutions generate solutions of the multitime reaction–diffusion PDE.

Keywords: multitime reaction–diffusion PDE; oblique derivative; exact solutions; first integrals (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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