The Cauchy Problem and Parabolic Boundary Value Problems in Spaces of Smooth Functions

1998 ◽  
pp. 181-232
Author(s):  
Samuil D. Eidelman ◽  
Nicolae V. Zhitarashu
Keyword(s):  
Cauchy Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Smooth Functions ◽  
Parabolic Boundary ◽  
The Cauchy Problem ◽  
Parabolic Boundary Value Problems

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.

Nonlocal Parabolic Boundary-Value Problems with Singularities

2015 ◽  
Vol 208 (3) ◽  
pp. 327-343 ◽  
Author(s):  
І. D. Pukal’s’kyi ◽  
I. M. Isaryuk
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Parabolic Boundary ◽  
Parabolic Boundary Value Problems

scholarly journals On the Exact Series Solution for Nonhomogeneous Strongly Coupled Mixed Parabolic Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Vicente Soler ◽  
Emilio Defez ◽  
Roberto Capilla ◽  
José Antonio Verdoy
Keyword(s):  
Boundary Value Problems ◽  
Series Solution ◽  
Boundary Value ◽  
Block Matrix ◽  
Coupled Systems ◽  
Parabolic Boundary ◽  
Strongly Coupled ◽  
Parabolic Boundary Value Problems ◽  
Stable Matrix

An exact series solution for nonhomogeneous parabolic coupled systems of the typeut-Auxx=Gx, t, A1u0, t+B1ux0, t=0, A2ul, t+B2uxl, t=0, 0<x<1, t>0, ux, 0=fx, whereA1, A2, B1, andB2are arbitrary matrices for which the block matrix is nonsingular, andAis a positive stable matrix, is constructed.

Sign in / Sign up

Export Citation Format

Share Document