In this paper, following the ideas of Lax, we prove a blow-up result for a class of solutions of the equation & -&x -&+xx -= 0, corresponding, in certain cases, to the development of a singularity in the second derivatives of 4. These solutions solve locally (in time) the Cauchy problem for smooth i
On the Multiplicity of Solutions of Semilinear Equations
β Scribed by Philip Korman
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 145 KB
- Volume
- 229
- Category
- Article
- ISSN
- 0025-584X
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π SIMILAR VOLUMES
## One-dimensionality of Solutions of Semilinear Elliptic Problems in Cylindrical Domains Let w be a bounded domain in R nΓI with smooth boundary, a > H; u AE P R, and let u P C I Γa; a Γ " w satisfy Γrgjruj jruj ΓI ru fx
In this paper we present exact solutions of the Klein-Gordon and the Dirac equations in different configurations of an electromagnetic field, which are characteristic for free-electron lasertype gauges. I n the case of motion of a charged scalar particle in standing wave an energy spectrum is studie
Weak solution of the Euler equations is defined as an L 2 -vector field satisfying the integral relations expressing the mass and momentum balance. Their general nature has been quite unclear. In this work an example of a weak solution on a 2-dimensional torus is constructed that is identically zero