Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena

DOI10.1007/BF00580702zbMath0562.35008MaRDI QIDQ2266813

Publication date: 1985

Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)

conservation laws thermodynamics symmetries shock waves acoustics gas dynamics mechanics singularities of maps geometrical theory smooth multivalued solutions

Mathematics Subject Classification ID

Analyticity in context of PDEs (35A20) Nonlinear higher-order PDEs (35G20) Geometric theory, characteristics, transformations in context of PDEs (35A30) Catastrophe theory (58K35) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Propagation of singularities; initial value problems on manifolds (58J47)

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Singularities of algebraic differential equations ⋮ Meta-symplectic geometry of \(3^{\mathrm{rd}}\) order Monge-Ampère equations and their characteristics ⋮ From symmetries of partial differential equations towards secondary (``quantized) calculus ⋮ Eikonal type equations for geometrical singularities of solutions in field theory ⋮ Control of displacement front in a model of immiscible two-phase flow in porous media ⋮ Geometric theory of singularities of solutions of nonlinear differential equations ⋮ Characteristics, bicharacteristics and geometric singularities of solutions of PDEs ⋮ Minkowski metrics on solutions of the Khokhlov-Zabolotskaya equation ⋮ Critical phenomena in filtration processes of real gases ⋮ Formation and propagation of singularities in one-dimensional Chaplygin gas ⋮ Geometric theory of special modes in the distributed-parameter control systems ⋮ Geometric study of gas behavior in a one-dimensional nozzle (the case of the van der Waals gas) ⋮ Shock waves in Euler flows of gases ⋮ Extensions of the Poisson bracket to differential forms and multi-vector fields ⋮ Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods ⋮ Mass and heat transport in the two-phase Buckley-Leverett model ⋮ Singularities in one-dimensional Euler flows

Cites Work

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