Academic Journal
On the Invariant Subspace Method for Nonlinear Second-Order Evolution Equations.
| Τίτλος: | On the Invariant Subspace Method for Nonlinear Second-Order Evolution Equations. |
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| Συγγραφείς: | Badgaish, Manal1 (AUTHOR), Hmidouch, Lhoucine2 (AUTHOR), Hmidouch, Nacir3 (AUTHOR) nhmidouch@talladega.edu |
| Πηγή: | Mathematics (2227-7390). Jun2026, Vol. 14 Issue 12, p2155. 14p. |
| Θεματικοί όροι: | *Invariant subspaces, *Nonlinear evolution equations, *Ordinary differential equations, *Reduced-order models, *Transport equation, *Reaction-diffusion equations, *Analytical solutions |
| Περίληψη: | We investigate invariant finite-dimensional linear spaces for a class of nonlinear evolution equations with second-order time dependence of the type ∂ t t u = − ∂ x (A (x , u) u) + ∂ x x (B (x , u) u) + f (u) , where the coefficients may depend nonlinearly on the solution. Using direct algebraic verification and invariant subspace reductions, we derive several exact solutions and reduce the governing equations to finite-dimensional systems of ordinary differential equations. Various examples are presented to illustrate the applicability of the method to nonlinear transport, diffusion, and reaction models. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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