Application of splines to the approximate determination of the classical solution of the Cauchy problem for a second-order quasilinear equation

1987 ◽  
Vol 39 (4) ◽  
pp. 405-410
Author(s):  
Khoang Van Lai
Keyword(s):  
Cauchy Problem ◽  
Classical Solution ◽  
Quasilinear Equation ◽  
Second Order ◽  
Approximate Determination ◽  
The Cauchy Problem

scholarly journals Nonlinear conservation laws for the Schrödinger boundary value problems of second order

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ming Ren ◽  
Shiwei Yun ◽  
Zhenping Li
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Maximum Modulus ◽  
Second Order ◽  
Nonlinear Conservation Laws ◽  
The Cauchy Problem ◽  
Modulus Method ◽  
Semilinear Schrödinger Equation

AbstractIn this paper, we apply a reliable combination of maximum modulus method with respect to the Schrödinger operator and Phragmén–Lindelöf method to investigate nonlinear conservation laws for the Schrödinger boundary value problems of second order. As an application, we prove the global existence to the solution for the Cauchy problem of the semilinear Schrödinger equation. The results reveal that this method is effective and simple.

Determination of a part of boundary for the Cauchy problem for the Laplace equation

2010 ◽  
Vol 18 (4) ◽  
pp. 535-548 ◽  
Author(s):  
Ji-Chuan Liu ◽  
Ting Wei
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
The Cauchy Problem

The cauchy problem for weakly hyperbolic equations of second order

1980 ◽  
Vol 5 (12) ◽  
pp. 1273-1296 ◽  
Author(s):  
Tatsuo Nishitani
Keyword(s):  
Cauchy Problem ◽  
Hyperbolic Equations ◽  
Second Order ◽  
The Cauchy Problem

scholarly journals The Randomized American Option as a Classical Solution to the Penalized Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Guillaume Leduc
Keyword(s):  
Cauchy Problem ◽  
Brownian Motion ◽  
Classical Solution ◽  
Penalty Method ◽  
Infinitesimal Generator ◽  
American Option ◽  
Geometric Brownian Motion ◽  
Uniform Bound ◽  
Option Value ◽  
The Cauchy Problem

We connect the exercisability randomized American option to the penalty method by showing that the randomized American option valueuis the uniqueclassicalsolution to the Cauchy problem corresponding to thecanonicalpenalty problem for American options. We also establish a uniform bound forAu, whereAis the infinitesimal generator of a geometric Brownian motion.

scholarly journals The Cauchy Problem for the Generalized Fractional Second Order Semilinear Evolution Equation

2020 ◽  
Author(s):  
Félix Pedro Q. Gómez ◽  
Ruy Coimbra Charão
Keyword(s):  
Cauchy Problem ◽  
Evolution Equation ◽  
Second Order ◽  
The Cauchy Problem

scholarly journals Find A General Solution Of An Equation Of The Hyperbolic Type With A Second-Order Singular Coefficient And Solve The Cauchy Problem Posed For This Equation.

2021 ◽  
Vol 25 (1) ◽  
pp. 80
Author(s):  
Karimova Shalola Musayevna ◽  
Melikuzieva Dilshoda Mukhtorjon qizi
Keyword(s):  
Cauchy Problem ◽  
General Solution ◽  
Type Equation ◽  
Second Order ◽  
Hyperbolic Type ◽  
Singular Coefficient ◽  
The Cauchy Problem

This paper presents a general solution of a hyperbolic type equation with a second-order singular coefficient and a solution to the Cauchy problem posed for this equation.

scholarly journals An iterative method for the Cauchy problem for second-order elliptic equations

2018 ◽  
Vol 142-143 ◽  
pp. 216-223 ◽  
Author(s):  
George Baravdish ◽  
Ihor Borachok ◽  
Roman Chapko ◽  
B. Tomas Johansson ◽  
Marián Slodička
Keyword(s):  
Cauchy Problem ◽  
Iterative Method ◽  
Elliptic Equations ◽  
Second Order ◽  
The Cauchy Problem ◽  
Second Order Elliptic Equations

Spectral Properties of the Cauchy Problem for a Second-Order Operator with Involution

2021 ◽  
Vol 57 (1) ◽  
pp. 1-10
Author(s):  
L. V. Kritskov ◽  
V. L. Ioffe
Keyword(s):  
Cauchy Problem ◽  
Spectral Properties ◽  
Second Order ◽  
Order Operator ◽  
The Cauchy Problem

Solving a second-order algebro-differential equation with respect to the derivative

2021 ◽  
pp. 414-420
Author(s):  
Vladimir I. Uskov
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Rigid Body ◽  
Fredholm Operator ◽  
Arbitrary Dimension ◽  
Second Order ◽  
Index Zero ◽  
Second Order Differential Equations ◽  
The Cauchy Problem ◽  
One Step

We consider a second-order algebro-differential equation. Equations and systems of second-order differential equations describe the operation of an electronic triode circuit with feedback, rotation of a rigid body with a cavity, reading information from a disk, etc. The highest derivative is preceded by an irreversible operator. This is a Fredholm operator with index zero, kernel of arbitrary dimension, and Jordan chains of arbitrary lengths. Equations with irreversible operators at the highest derivative are called algebro-differential. In this case, the solution to the problem exists under certain conditions on the components of the desired function. To solve the equation with respect to the derivative, the method of cascade splitting of the equation is used, which consists in the stepwise splitting of the equation into equations in subspaces of decreasing dimensions. Cases of one-step and two-step splitting are considered. The splitting uses the result on the solution of a linear equation with Fredholm operator. In each case, the corresponding result is formulated as a theorem. To illustrate the result obtained in the case of one-step splitting, an illustrative example of the Cauchy problem is given.

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