Group theoretic and similarity analysis of hyperbolic partial differential equations

DOI10.1016/0022-247X(86)90067-3zbMath0602.35075MaRDI QIDQ1081758

Waclaw Frydrychowicz, Mansa C. Singh

Publication date: 1986

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

wave propagationtransformationsconformal invariancewavefrontcharacteristicsquasilinear second order equationsr-parameter groupsSimilarity analysis

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Second-order nonlinear hyperbolic equations (35L70) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (7)

Similarity representation of wave propagation in a nonlinear viscoelastic rod on a group theoretic basis ⋮ A nonlinear hyperbolic free boundary value problem ⋮ Application of one-parameter groups of transformation in mechanics ⋮ An implicit difference scheme for a moving boundary hyperbolic problem ⋮ A moving boundary hyperbolic problem for a stress impact in a bar of rate-type material ⋮ Group theoretic analysis and similarity solution for a nonlinear viscous rod subjected to time dependent velocity impact ⋮ Discontinuous solutions of nonlinear wave phenomena by similarity approach

Cites Work

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• Similarity methods for differential equations
• Some matrix aspects of generalized dimensional analysis
• Wave propagation in non-homogeneous thin elastic rods subjected to time dependent stress impact
• Wave propagation in nonhomogeneous thin elastic rods subjected to time-dependent velocity impact
• Reduction of the Number of Variables in Systems of Partial Differential Equations, with Auxiliary Conditions
• THE REDUCTION BY ONE OF THE NUMBER OF INDEPENDENT VARIABLES IN SOME SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS
• Differential Invariants and Invariant Partial Differential Equations Under Continuous Transformation Groups in Normed Linear Spaces

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