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Conservation Laws and Global Solutions of Linear First Order PDEs with Distributional Coefficients

✍ Scribed by C.O.R Sarrico

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
105 KB
Volume
257
Category
Article
ISSN
0022-247X

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✦ Synopsis

We treat linear partial differential equations of first order with distributional coefficients naturally related to physical conservation laws in the spirit of our Ž . preceding papers which concern ordinary differential equations : the solutions are consistent with the classical ones. Under compatibility conditions we prove uniqueness and existence results. As an example we consider the problem u q ␦ u s 0,

Ε½ X Ε½ 2 . ing D D ‫ޒ‬ is the space of distributions with discrete support and ␦ is the Dirac l l Ε½ ..

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We study the limit of the solution of linear and semilinear second order PDEs of parabolic type, with rapidly oscillating periodic coefficients, singular drift, and singular coefficient of the zeroth order term. Our method of proof is fully probabilistic and builds upon the arguments in earlier work