On nonnegative classical solutions of coupled Euler–Poisson–Darboux–Tricomi equations with nonlinear sources

Svetlin G. Georgiev; Safa M. Mirgani; Khaled Zennir; Keltoum Bouhali; Svetlin G. Georgiev; Safa M. Mirgani; Khaled Zennir; Keltoum Bouhali

doi:10.3934/math.2026229

AIMS Mathematics

2026, Volume 11, Issue 3: 5557-5574. doi: 10.3934/math.2026229

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Research article

On nonnegative classical solutions of coupled Euler–Poisson–Darboux–Tricomi equations with nonlinear sources

1.
Department of Mathematics, Sorbonne University, Paris, France; svetlingeorgiev1@gmail.com
2.
Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University, Riyadh 13318, Saudi Arabia; smmmohamed@imamu.edu.sa
3.
Departement of Mathematics, College of Sciences, Qassim University, Saudi Arabia; k.zennir@qu.edu.sa, k.bouhali@qu.edu.sa

Received: 26 January 2026 Revised: 21 February 2026 Accepted: 27 February 2026 Published: 05 March 2026
MSC : 55B44, 35L52, 35G55

We study the initial value problem for a class of coupled Euler–Poisson–Darboux–Tricomi equations with nonlinear source terms. Such systems arise in fluid dynamics, plasma physics, transonic flow, and wave propagation in inhomogeneous media. Using new integral representations of the solutions and appropriate fixed point theorems in Banach spaces, we establish the existence of at least one, at least two, and at least three nonnegative classical solutions under suitable conditions on the parameters and initial data. An illustrative example is provided to demonstrate the applicability of the main results.
- Euler–Poisson–Darboux–Tricomi equations,
- energy and industry,
- nonlinear equations,
- classical solutions,
- integral representations,
- iterative methods
Citation: Svetlin G. Georgiev, Safa M. Mirgani, Khaled Zennir, Keltoum Bouhali. On nonnegative classical solutions of coupled Euler–Poisson–Darboux–Tricomi equations with nonlinear sources[J]. AIMS Mathematics, 2026, 11(3): 5557-5574. doi: 10.3934/math.2026229

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Abstract

We study the initial value problem for a class of coupled Euler–Poisson–Darboux–Tricomi equations with nonlinear source terms. Such systems arise in fluid dynamics, plasma physics, transonic flow, and wave propagation in inhomogeneous media. Using new integral representations of the solutions and appropriate fixed point theorems in Banach spaces, we establish the existence of at least one, at least two, and at least three nonnegative classical solutions under suitable conditions on the parameters and initial data. An illustrative example is provided to demonstrate the applicability of the main results.

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