Nonlinear Partial Differential Equations Arising from Prescribed Curvature Problems

Differential Equations ◽

Scalar Curvature ◽

Nonlinear Pde ◽

Minkowski Problem ◽

Partial Differential ◽

Prescribed Curvature ◽

Nirenberg Problem ◽

Curvature Problem

We consider two prominent nonlinear partial differential equations (nonlinear PDE) linked to the prescribed curvature problems, namely, the Minkowski problem and the KazdanWarner/Nirenberg problem (prescribed scalar curvature problem). This article addresses some of the modern techniques in analysis used to draw out a number of the profound features in these equations.

Nonlinear Partial Differential Equations and Related Problems of Pade Approximations.

10.21236/ada141519 ◽

1983 ◽

Author(s):

D. V. Chudnovsky ◽

G. V. Chudnovsky

Keyword(s):

Differential Equations ◽

Padé Approximations ◽

Partial Differential ◽

Pade Approximations

Numerical and Analytical Methods in Nonlinear Partial Differential Equations.

10.21236/ada185210 ◽

1987 ◽

Author(s):

Richard E. Ewing

Keyword(s):

Differential Equations ◽

Analytical Methods ◽

Partial Differential ◽

Numerical And Analytical Methods

Proceedings of the Fourth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18–22 August 1993 ◽

Formation of Shocks for Nonlinear Partial Differential Equations of First Order

10.1515/9783112318874-022 ◽

1994 ◽

pp. 199-204

Keyword(s):

Differential Equations ◽

Partial Differential ◽

First Order

Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

Forum Mathematicum ◽

10.1515/forum-2020-0232 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Robert Stegliński

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Dirichlet Boundary ◽

Dirichlet Boundary Conditions ◽

Partial Differential ◽

Linear Partial Differential Equations ◽

Lyapunov Inequalities ◽

Funct Anal

Abstract The aim of this paper is to extend results from [A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), 1, 176–193] about Lyapunov-type inequalities for linear partial differential equations to nonlinear partial differential equations with 𝑝-Laplacian with zero Neumann or Dirichlet boundary conditions.

Analytical mathematical schemes: Circular rod grounded via transverse Poisson’s effect and extensive wave propagation on the surface of water

Open Physics ◽

10.1515/phys-2020-0163 ◽

2020 ◽

Vol 18 (1) ◽

pp. 545-554

Author(s):

Asghar Ali ◽

Aly R. Seadawy ◽

Dumitru Baleanu

Keyword(s):

Wave Propagation ◽

Differential Equations ◽

Longitudinal Wave ◽

Symbolic Computation ◽

Boussinesq Equation ◽

Wave Model ◽

Simple Equation ◽

Partial Differential

AbstractThis article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-\text{Ψ}(\xi ))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson’s effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.