Existence and Uniqueness in the Linearised One and Two-dimensional Problem of Partial Differential Equations With Variational Method

Authors

  • Bayu Prihandono Universitas Tanjungpura
  • Mariatul Kiftiah Universitas Tanjungpura
  • Yudhi Yudhi Universitas Tanjungpura

DOI:

https://doi.org/10.25077/jmua.11.3.141-158.2022

Abstract

The classical solution and the strong solution of a partial differential equation problem are continuously differentiable solutions. This solution has a derivative for a continuous infinity level. However, not all problems of partial differential equations can be easily obtained by strong solutions. Even the existence of a solution requires in-depth investigation. The variational formulation method can qualitatively analyze a single solution to a partial differential equation problem. This study provides an alternative method in analyzing the problem model of partial differential equations analytically. In this research, we will examine the partial differential equation modelling built from fluid dynamics modelling.

Author Biographies

Bayu Prihandono, Universitas Tanjungpura

Jurusan Matematika Fakultas MIPA

Mariatul Kiftiah, Universitas Tanjungpura

Jurusan Matematika Fakultas MIPA

Yudhi Yudhi, Universitas Tanjungpura

Jurusan Matematika Fakultas MIPA

References

H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext. Springer New York, 2010.

L. Evans. Partial Differential Equations. Graduate studies in mathematics. American Mathematical Society, 1997.

C. D. Pagani. The Neumann–Kelvin problem revisited. Applicable Analysis, 85(1-3):277–292, 2006.

C. D. Pagani and D. Pierotti. The Neumann–Kelvin problem for a beam. Journal of Mathematical Analysis and Applications, 240(1):60 – 79, 1999.

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Published

30-07-2022

Issue

Vol. 11 No. 3 (2022)

Section

Articles

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