scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

scholarly journals On a global classical solution of a quasilinear hyperbolic equation

1989 ◽  
Vol 12 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Y. Ebihara ◽  
D. C. Pereira
Keyword(s):  
Hyperbolic Equation ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Torsional Vibrations ◽  
Global Classical Solution ◽  
Quasilinear Hyperbolic Equation ◽  
Global Classical Solutions

In this paper we establish the existence and uniqueness of global classical solutions for the equation which arises in the study of the extensional vibrations of thin rod, or torsional vibrations of thin rod.

scholarly journals Global classical solutions to the Cauchy problem for a nonlinear wave equation

1998 ◽  
Vol 21 (3) ◽  
pp. 533-548 ◽  
Author(s):  
Haroldo R. Clark
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Classical Solution ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Global Classical Solution ◽  
Global Classical Solutions ◽  
The Cauchy Problem

In this paper we consider the Cauchy problem{u″+M(|A12u|2)Au=0   in   ]0,T[u(0)=u0,       u′(0)=u1,whereu′is the derivative in the sense of distributions and|A12u|is theH-norm ofA12u. We prove the existence and uniqueness of global classical solution.

A REACTION INFILTRATION PROBLEM: EXISTENCE, UNIQUENESS, AND REGULARITY OF SOLUTIONS IN TWO SPACE DIMENSIONS

1995 ◽  
Vol 05 (05) ◽  
pp. 599-618 ◽  
Author(s):  
JOHN CHADAM ◽  
XINFU CHEN ◽  
ROBERTO GIANNI ◽  
RICCARDO RICCI
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Partial Regularity ◽  
Regularity Of Solutions ◽  
Infinite Strip ◽  
Two Dimensional ◽  
Finite Strip ◽  
Two Space Dimensions

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. We establish global existence, uniqueness and regularity of the solution in a two-dimensional finite strip (−M, M)×(0, 1) and the existence and partial regularity of solutions in an infinite strip (−∞, ∞)×(0, 1).

Generalized plane stress in a semi-infinite strip under arbitrary end-load

1964 ◽  
Vol 281 (1385) ◽  
pp. 184-206 ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Plane Stress ◽  
Stress Function ◽  
Infinite Strip ◽  
Order Ordinary Differential Equation ◽  
Orthogonal Functions

The problem involves the determination of a biharmonic generalized plane-stress function satisfying certain boundary conditions. We expand the stress function in a series of non-orthogonal eigenfunctions. Each of these is expanded in a series of orthogonal functions which satisfy a certain fourth-order ordinary differential equation and the boundary conditions implied by the fact that the sides are stress-free. By this method the coefficients involved in the biharmonic stress function corresponding to any arbitrary combination of stress on the end can be obtained directly from two numerical matrices published here The method is illustrated by four examples which cast light on the application of St Venant’s principle to the strip. In a further paper by one of the authors, the method will be applied to the problem of the finite rectangle.

COEFFICIENT INVERSE PROBLEMS FOR THE PARABOLIC EQUATION WITH GENERAL WEAK DEGENERATION

2021 ◽  
Vol 9 (1) ◽  
pp. 91-106
Author(s):  
N. Huzyk ◽  
O. Brodyak
Keyword(s):  
Parabolic Equation ◽  
Inverse Problems ◽  
Existence And Uniqueness ◽  
Space Variable ◽  
Time Derivative ◽  
Classical Solutions ◽  
Linear Polynomial ◽  
Coefficient Inverse Problems ◽  
Degenerate Parabolic ◽  
Increasing Function

It is investigated the inverse problems for the degenerate parabolic equation. The mi- nor coeffcient of this equation is a linear polynomial with respect to space variable with two unknown time-dependent functions. The degeneration of the equation is caused by the monotone increasing function at the time derivative. It is established conditions of existence and uniqueness of the classical solutions to the named problems in the case of weak degeneration.

scholarly journals Extreme Analysis of a Random Ordinary Differential Equation

2014 ◽  
Vol 51 (4) ◽  
pp. 1021-1036 ◽  
Author(s):  
Jingchen Liu ◽  
Xiang Zhou
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Elliptic Equation ◽  
Gaussian Process ◽  
Stochastic System ◽  
Random Coefficient ◽  
Asymptotic Approximations ◽  
Tail Probabilities ◽  
One Dimensional ◽  
Spatially Varying

In this paper we consider a one dimensional stochastic system described by an elliptic equation. A spatially varying random coefficient is introduced to account for uncertainty or imprecise measurements. We model the logarithm of this coefficient by a Gaussian process and provide asymptotic approximations of the tail probabilities of the derivative of the solution.

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