Results 201 to 210 of about 99,299 (234)
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Partial Differential Equations of Elliptic Type
2004In the present chapter we consider the well-posedness of an abstract boundary-value problem for differential equations of elliptic type $$- \upsilon ''\left( t \right) + A\upsilon \left( t \right) = f\left( t \right)\left( {0 \leqslant t \leqslant T} \right),\upsilon \left( 0 \right) = {{\upsilon }_{0}},\upsilon \left( T \right) = {{\upsilon }_{T}}$$
Pavel E. Sobolevskii +1 more
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Determination of a coefficient in an elliptic partial differential equation
Journal of Inverse and Ill-Posed Problems, 1995Summary: The existence and uniqueness theorems for the problem of finding one of the coefficients \(a(x)\), \(c(x)\), \(q(x)\) and the unknown function \(u(x,y)\) in the equations \[ \bigl( a(x) u_ x (x,y) \bigr)_ x + \bigl( b(x) u_ y(x,y) \bigr)_ y - c(x) u(x,y) = q(x) f(x,y),\;0 < x < X,\;0 < y < Y, \] \[ u(0,y) = \varphi (y),\;0 < y \leq Y,\;u_ x (0,
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Convexity of Solutions to Some Elliptic Partial Differential Equations
SIAM Journal on Mathematical Analysis, 1993The authors reprove a result of \textit{A. U. Kennington} [Indiana Univ. Math. J. 34, 687-704 (1985; Zbl 0566.35025)] which states that the concavity function \(C\) of solutions \(v\) to elliptic equations \(a^{ij}(Dv)v_{ij}=b(x,v,Dv)\) cannot have a local positive maximum in \(\Omega \times \Omega\). The new proof makes use of a stronger assumption \((
GRECO, ANTONIO, PORRU GIOVANNI
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Linear Elliptic Partial Differential Equations
2017In earlier chapters, we described how to apply the finite element method to ordinary differential equations. For the remainder of this book, we will focus on extending this technique for application to partial differential equations. As with ordinary differential equations, we begin with a simple example to illustrate the key features.
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Partial differential equations of multi-quasi-elliptic type
ANNALI DELL UNIVERSITA DI FERRARA, 1999Summary: The theory of multi-quasi-elliptic operators and associated Sobolev spaces is revised in this article and possible directions for research are indicated concerning operators of principal type and nonlinear equations. Moreover, some new results concerning operators with anti-Wick symbols are presented.
BOGGIATTO, Paolo, RODINO, Luigi Giacomo
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Nonlinear Elliptic Partial Differential Equations
2017In Chap. 5, we explained how to apply the finite element method to nonlinear ordinary differential equations. We saw that calculating the finite element solution of nonlinear differential equations required us to solve a nonlinear system of algebraic equations and discussed how these algebraic equations could be solved.
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Viscosity solutions of elliptic partial differential equations
1998Summary: In my talk and its associated paper I discuss some recent results connected with the uniqueness of viscosity solutions of nonlinear elliptic and parabolic partial differential equations. By now, most researchers in partial differential equations are familiar with the definition of viscosity solution, introduced by \textit{M. G.
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Some Nonlinear Elliptic Partial Differential Equations and Difference Equations
Journal of the Society for Industrial and Applied Mathematics, 1964Abstract : The Dirichlet problem for the non-linear elliptic partial differential equation a(x,y,u(x,y))u, sub xx + c(x,y,u(x,y))u, sub yy - gamma(x, y,u(x,y))u = O is studied. It is assumed that the coefficients are strictly positive and Lipschitz in the argument u(x,y). It is then proved that the solution may be uniformly approximated by the solution
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Double image encryption algorithm based on compressive sensing and elliptic curve
AEJ - Alexandria Engineering Journal, 2022Guo-dong Ye
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