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"This book presents a hands-on approach to numerical continuation and bifurcation for nonlinear PDEs" [Publisher]

Differential equations, Nonlinear --- Équations différentielles non linéaires --- Numerical solutions. --- Solutions numériques

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Runge-Kutta formulas. --- Runge-Kutta methods --- Differential equations --- Numerical solutions --- Fórmules de Runge-Kutta --- Mètodes de Runge-Kutta

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"We study 2D compressible Euler flows in bounded impermeable domains whose boundary is smooth except for corners. We assume that the angles of the corners are small enough. Then we obtain local (in time) existence of solutions which keep the L2 Sobolev regularity of their Cauchy data, provided the external forces are sufficiently regular and suitable compatibility conditions are satisfied. Such a result is well known when there is no corner. Our proof relies on the study of associated linear problems. We also show that our results are rather sharp: we construct counterexamples in which the smallness condition on the angles is not fulfilled and which display a loss of L2 Sobolev regularity with respect to the Cauchy data and the external forces"--

Boundary value problems --- Differential equations, Hyperbolic. --- Gas dynamics --- Équations différentielles hyperboliques --- Problèmes aux limites --- Gaz, Dynamique des --- Numerical solutions. --- Solutions numériques --- Lagrange equations --- Mathematics.

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Stochastic differential equations. --- Differential equations, Partial --- Mathematical physics. --- Numerical solutions. --- Physical mathematics --- Physics --- Numerical analysis --- Differential equations --- Fokker-Planck equation --- Mathematics