Results 21 to 30 of about 221 (109)
Relative entropy in diffusive relaxation [PDF]
, 2012 We establish convergence in the diffusive limit from entropy weak solutions of the equations of compressible gas dynamics with friction to the porous media equation away from vacuum.
Tzavaras, Athanasios E. +1 more
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On Critical Behaviour in Systems of Hamiltonian Partial Differential Equations [PDF]
, 2015 We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components.
Klein, Christian +13 more
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Periodic Solutions of Quasi-Monotone Semilinear Multidimensional Hyperbolic Systems [PDF]
, 2023 This paper deals with the Cauchy problem for a class of first-order semilinear hyperbolic equations of the form ∂tfi+∑j=1dλij∂xjfi=Qi(f). where fi=fi(x,t) (i=1,⋯,n) and x=(x1,⋯,xd)∈IRd (n≥2,d≥1). Under assumption of the existence of a conserved quantity ∑
Corrado Mascia, Mascia C.
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Curvelets, Wave Atoms, and Wave Equations [PDF]
, 2006 We argue that two specific wave packet families---curvelets and wave atoms---provide powerful tools for representing linear systems of hyperbolic differential equations with smooth, time-independent coefficients.
Demanet, Laurent
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A two-component nonlinear variational wave system [PDF]
, 2023 We derive a novel two-component generalization of the nonlinear variational wave equation as a model for the director field of a nematic liquid crystal with a variable order parameter. The equation admits classical solutions locally in time.
Aursand, Peder Kristian +1 more
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Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations [PDF]
, 1993 summary:We consider three types of semilinear second order PDEs on a cylindrical domain $\Omega \times (0,\infty )$, where $\Omega $ is a bounded domain in ${{\mathbb{R}}}^N$, $N\ge 2$.
Poláčik, P. +4 more
core +1 more source
From Stability to Chaos: A Complete Classification of the Damped Klein‐Gordon Dynamics
Mathematical Methods in the Applied Sciences, Volume 49, Issue 9, Page 9696-9708, June 2026.ABSTRACT We investigate the transition between stability and chaos in the damped Klein‐Gordon equation, a fundamental model for wave propagation and energy dissipation. Using semigroup methods and spectral criteria, we derive explicit thresholds that determine when the system exhibits asymptotic stability and when it displays strong chaotic dynamics ...
Carlos Lizama +2 more
wiley +1 more source
, 2020 In this paper, we study the existence of mild periodic solutions of abstract semilinear equations in a setting that includes several other types of equations such as delay differential equations, first-order hyperbolic partial differential equations, and
Ruan, Shigui, Su, Qiuyi
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Multiple front and pulse solutions in spatially periodic systems
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract In this paper, we develop a comprehensive mathematical toolbox for the construction and spectral stability analysis of stationary multiple front and pulse solutions to general semilinear evolution problems on the real line with spatially periodic coefficients.
Lukas Bengel, Björn de Rijk
wiley +1 more source
Existence of Weak Solutions for a Degenerate Goursat‐Type Linear Problem
Mathematical Methods in the Applied Sciences, Volume 48, Issue 15, Page 14334-14341, October 2025.ABSTRACT For a generalization of the Gellerstedt operator with mixed‐type Dirichlet boundary conditions to a suitable Tricomi domain, we prove the existence and uniqueness of weak solutions of the linear problem and for a generalization of this problem.
Olimpio Hiroshi Miyagaki +2 more
wiley +1 more source