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2013
In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking.
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In this chapter we study the Cauchy problems for one-dimensional scalar conservation laws. In particular, we prove that the Cauchy problem is well posed in the class of entropy weak solutions, in the sense that it admits a unique entropy weak solution. The existence of the solutions is proved by the method of wave front tracking.
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Asymptotics of solutions of a cauchy problem
Ukrainian Mathematical Journal, 1991See the review in Zbl 0727.34037.
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1970
Cauchy’s problem with holomorphic data can be studied at the characteristic points of the hypersurface S carrying Cauchy’s data; (for linear equations, see [4], which improves [3; I]; for non linear equations, see Y. Choquet-Bruhat [1]). In general its solution u is algebroid at those points (but an equation with constant coefficients and constant data
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Cauchy’s problem with holomorphic data can be studied at the characteristic points of the hypersurface S carrying Cauchy’s data; (for linear equations, see [4], which improves [3; I]; for non linear equations, see Y. Choquet-Bruhat [1]). In general its solution u is algebroid at those points (but an equation with constant coefficients and constant data
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New transformations of Cauchy matrices and Trummer's problem
Computers and Mathematics With Applications, 1998V Y Pan
exaly
Nonlocal Cauchy problem for fractional evolution equations
Nonlinear Analysis: Real World Applications, 2010Yong Zhou, Feng Jiao
exaly
Two regularization methods for a Cauchy problem for the Laplace equation
Journal of Mathematical Analysis and Applications, 2008Zhi Qian, Chu-Li Fu
exaly
The global Cauchy problem for the NLS and NLKG with small rough data
Journal of Differential Equations, 2007Henryk Hudzik
exaly