Applicable Analysis and Discrete Mathematics, Vol. 17, No. 2 (October, 2023), pp. 480-495 (16 pages) This paper is divided in two parts. In the first part, we prove coercivity results and minimization ...

In this paper, we first establish a principle of concentration compactness in $W^{1,p(x)}({\Bbb R}^{N})$ . Then, based on this concentration compactness principle, we ...

Studies properties and solutions of partial differential equations. Covers methods of characteristics, well-posedness, wave, heat and Laplace equations, Green's functions, and related integral ...

In the past few decades, the use of phase field-modeling equations for mathematical modeling has progressed. Phase separation has been studied extensively in thermodynamics and materials engineering, ...

Reviews ordinary differential equations, including solutions by Fourier series. Physical derivation of the classical linear partial differential equations (heat, wave, and Laplace equations). Solution ...