The Problem of Non-Smooth Solutions for a Type of Parabolic Complex Equations

Guang Shan Xu; Zhong Tai Ma

doi:10.4028/www.scientific.net/AMM.40-41.877

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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vols. 40-41The Problem of Non-Smooth Solutions for a Type of...

The Problem of Non-Smooth Solutions for a Type of Parabolic Complex Equations

Abstract:

In this paper, the problem of non-smooth properties for a type of general second order parabolic type equation is discussed and the result-------there are C∞-functions f for which we consider the equation that has no C2-solutions is proved by using a method of function construction, moreover, the dependent relations between the solution u and the diffusion term f is given.

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Periodical:

Applied Mechanics and Materials (Volumes 40-41)

Pages:

877-880

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.40-41.877

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Online since:

November 2010

Authors:

Guang Shan Xu, Zhong Tai Ma

Keywords:

Cauchy-Kowaleski Theorem, Holomorphic Solution, Parabolic Type Complex Equation, Schwarz Reflection Principle

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References

[1] V. Egorov. On the solvability of differential equation with simple characteristics, Russian Math. Surveys, Vol. 26 (1971), pp.113-130.

Google Scholar

[2] P. Garabedian. An unsolvable problem, Proc. Amer. Math. Soc., Vol. 25 (1970), pp.207-208.

Google Scholar

[3] P. Garabedian. Partial differential equations, Wiley, New York, (1964).

Google Scholar

[4] V. Grushin. A certain example of a differential equation without solutions, Math. Notes, Vol. 10 (1971), pp.499-501.

Google Scholar

[5] L. Hormander. Linear partial differential operators, Berlin, Springer-Verlag, (1963).

Google Scholar

[6] H. Lewy. An example of a smooth linear partial differential equation, Ann. Math., Vol. 66 (1957), pp.617-628.

Google Scholar

[7] L. Nirberg. Lectures on linear Partial differential equations, Providence, R. I., American Math. Society, (1973).

Google Scholar

[8] L. Nirberg and F. Treves. On local solvability of linear Partial differential equations, I, Necessary conditions, Comm. Pure. Appl. Math., Vol. 23, (1970), pp.1-38.

DOI: 10.1002/cpa.3160230102

Google Scholar

[9] L. Nirberg and F. Treves. On local solvability of linear Partial differential equations, II, Sufficient conditions, Comm. Pure. Appl. Math., Vol. 23, (1970), pp.459-510.

DOI: 10.1002/cpa.3160230314

Google Scholar