A comparison is given of the estimates of the existence times of "smooth" solutions of a quasilinear hyperbolic system in the Courant-Lax canonic form, following asuitably modified version of Cesari’s [2] and Borovikov’s [6] theories. The results can be applied to the dynamics of inviscid compressible fluids.
A periodic BVP for a semilinear elliptic-parabolic equation in an unbounded domain contained in a half-space of is considered, with Dirichlet boundary conditions on the finite part of . A theorem of uniqueness of periodic solutions is proved by showing that a suitable function of the "energy" is subharmonic in and satisfies a Phragmèn-Lindelöf growth condition at infinity.
A periodic BVP for a semilinear elliptic-parabolic equation in an unbounded domain contained in a half-space of is considered, with Dirichlet boundary conditions on the finite part of . A theorem of uniqueness of periodic solutions is proved by showing that a suitable function of the "energy" is subharmonic in and satisfies a Phragmèn-Lindelöf growth condition at infinity.
A survey of topical results is presented concerning BVPs for quasilinear hyperbolic systems in bicharacteristic form arising from the phenomenon of the duplication of frequency of laser radiation through a nonlinear medium. Cesari's existence proof is outlined together with ensuing iterative methods. Original numerical results for ruby red laser radiation through a quartz crystal are also included.
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