Advances in Nonlinear Partial Differential Equations and Stochastics
In 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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The Null Condition and Global Existence of Solutions
Scaling Limits for Large Systems of Interacting Particles
Regularity of Solutions of Initial Boundary Value Problems
On the HalfSpace Problem for the Discrete Velocity
Blowup Life Span and Large Time Behavior of Solutions to
On a Decay Rate of Solutions to OneDimensional Thermoelastic
Bifurcation Phenomena for the Duffing Equation
Some Remarks on the Compactness Method
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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