On a priori estimate in Wq1,2 for the solution of nondivergent parabolic equation with unbounded coefficients

2016 ◽  
Author(s):  
V. L. Kamynin ◽  
T. I. Bukharova
Keyword(s):  
Parabolic Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate ◽  
Unbounded Coefficients

scholarly journals Mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator

2002 ◽  
Vol 15 (3) ◽  
pp. 277-286 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Continuous Dependence ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Bessel Operator ◽  
Analysis Method ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we prove the existence, uniqueness and continuous dependence on the data of a solution of a mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator. The proof uses a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the considered problem.

scholarly journals On weak solutions of semilinear hyperbolic-parabolic equations

1996 ◽  
Vol 19 (4) ◽  
pp. 751-758 ◽  
Author(s):  
Jorge Ferreira
Keyword(s):  
Parabolic Equation ◽  
Continuous Function ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
A Priori ◽  
A Priori Estimate ◽  
Dirichlet Boundary Conditions ◽  
Priori Estimate

In this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equation(K1(x,t)u′)′+K2(x,t)u′+A(t)u+F(u)=fwith null Dirichlet boundary conditions and zero initial data, whereF(s)is a continuous function such thatsF(s)≥0,∀s∈Rand{A(t);t≥0}is a family of operators ofL(H01(Ω);H−1(Ω)). For the existence we apply the Faedo-Galerkin method with an unusual a priori estimate and a result of W. A. Strauss. Uniqueness is proved only for some particular classes of functionsF.

scholarly journals A Mixed Problem with an Integral Two-Space-Variables Condition for Parabolic Equation with The Bessel Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Bouziani Abdelfatah ◽  
Oussaeif Taki-Eddine ◽  
Ben Aoua Leila
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Space ◽  
A Priori ◽  
Energy Inequality ◽  
A Priori Estimate ◽  
Bessel Operator ◽  
Priori Estimate ◽  
Uniqueness Of The Solution

We study a mixed problem with an integral two-space-variables condition for parabolic equation with the Bessel operator. The existence and uniqueness of the solution in functional weighted Sobolev space are proved. The proof is based on a priori estimate “energy inequality” and the density of the range of the operator generated by the problem considered.

scholarly journals A locally one-dimensional scheme for a general parabolic equation describing microphysical processes in convective clouds

2021 ◽  
Vol 21 (4) ◽  
pp. 45-55
Author(s):  
B.A. Ashabokov ◽  
◽  
A.Kh. Khibiev ◽  
M.Kh. Shkhanukov-Lafishev ◽  
◽  
...  
Keyword(s):  
Parabolic Equation ◽  
Difference Scheme ◽  
A Priori ◽  
A Priori Estimate ◽  
Priori Estimate ◽  
One Dimensional ◽  
Convective Clouds ◽  
Non Local ◽  
Microphysical Processes

A locally one-dimensional difference scheme for a general parabolic equation in a p-dimensional parallelepiped is considered. To describe microphysical processes in convective clouds, non-local (nonlinear) integral sources of a special type are included in the equation under consideration. An a priori estimate for the solution of a locally one-dimensional scheme is obtained and its convergence is proved.

scholarly journals A PRIORI ESTIMATE FOR AN EQUATION WITH FRACTIONAL DERIVATIVES WITH DIFFERENT ORIGINS

2019 ◽  
pp. 41-47
Author(s):  
Л.М. Энеева
Keyword(s):  
Fractional Derivatives ◽  
Model Equation ◽  
A Priori ◽  
A Priori Estimate ◽  
Equation Of Motion ◽  
Point Boundary ◽  
Priori Estimate ◽  
Fractal Media ◽  
Different Origins ◽  
Variable Potential

В работе исследуется обыкновенное дифференциальное уравнение дробного порядка, содержащее композицию дробных производных с различными началами, с переменным потенциалом. Рассматриваемое уравнение выступает модельным уравнением движения во фрактальной среде. Для исследуемого уравнения доказана априорная оценка решения смешанной двухточечной краевой задачи. We consider an ordinary differential equation of fractional order with the composition of leftand right-sided fractional derivatives, and with variable potential. The considered equation is a model equation of motion in fractal media. We prove an a priori estimate for solutions of a mixed two-point boundary value problem for the equation under study.

scholarly journals A Discrete Analog of the Lyapunov Function for Hyperbolic Systems

2018 ◽  
Vol 64 (4) ◽  
pp. 591-602
Author(s):  
R D Aloev ◽  
M U Khudayberganov
Keyword(s):  
Lyapunov Function ◽  
Hyperbolic Systems ◽  
A Priori ◽  
A Priori Estimate ◽  
Discrete Analog ◽  
Priori Estimate ◽  
Constant Coefficients ◽  
The Difference ◽  
Dissipative Boundary ◽  
Linear Hyperbolic System

We study the difference splitting scheme for the numerical calculation of stable solutions of a two-dimensional linear hyperbolic system with dissipative boundary conditions in the case of constant coefficients with lower terms. A discrete analog of the Lyapunov function is constructed and an a priori estimate is obtained for it. The obtained a priori estimate allows us to assert the exponential stability of the numerical solution.

Sign in / Sign up

Export Citation Format

Share Document