## Advances in Nonlinear Partial Differential Equations and StochasticsIn the past two decades, there has been great progress in the theory of nonlinear partial differential equations. This book describes the progress, focusing on interesting topics in gas dynamics, fluid dynamics, elastodynamics etc. It contains ten articles, each of which discusses a very recent result obtained by the author. Some of these articles review related results. |

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### Contents

The Null Condition and Global Existence of Solutions | 43 |

Scaling Limits for Large Systems of Interacting Particles | 87 |

Regularity of Solutions of Initial Boundary Value Problems | 133 |

On the HalfSpace Problem for the Discrete Velocity | 160 |

Blowup Life Span and Large Time Behavior of Solutions to | 175 |

On a Decay Rate of Solutions to OneDimensional Thermoelastic | 198 |

Bifurcation Phenomena for the Duffing Equation | 292 |

Some Remarks on the Compactness Method | 319 |

### Other editions - View all

Advances in Nonlinear Partial Differential Equations and Stochastics S Kawashima,T Yanagisawa Limited preview - 1998 |

### Common terms and phrases

apply assume assumption Banach space bifurcation points Boltzmann equation bond percolation boundary condition boundary value problem bounded Cauchy problem coefficients coming flow compactness completes the proof consider continuous functions contraction mappings converges define denote density derivatives differential equations discrete velocity models domain drds duality argument edge eigenvalue exist countably finite following theorem formula global existence Hence holds hyperbolic systems implies inequality initial boundary value initial value problem integral lattice limit linear Math Mathematics matrix Moreover nonlinear null condition obtain particles percolation period-doubling bifurcation periodic solution positive constants pre-Sierpinski gasket proof of Theorem Proposition prove quasilinear resp respectively right-hand side satisfies sequence Shizuta shock front shock polar Sierpinski gaskets smooth Sobolev spaces supersonic flow past Suppose T-periodic tangential term theory uniformly variable vector wave equations weak solution wing Young measure