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Singularities of Solutions of Singular Integral Equations
Ukrainian Mathematical Journal, 2002This paper deals with a singular integral equation \[ Sq+Tq=f,\tag{1} \] where \(q(x)\) is an unknown function, \[ Sq(x):=aq(x)+\frac{1}{\pi }\text{v.p.} \int_{-1}^{1} \frac{q(\tau)}{\tau -x} d\tau,\;Tq(x):=\int_{-1}^{1}K(x,\tau)q(\tau) d\tau. \] It is assumed that the functions \(f\) and \(K\) smoothly depend on additional parameters.
V. E. Kapustyan, V. M. Il'man
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Singular solutions in elasticity [PDF]
Acta Mechanica, 1967 General solutions of the time-independent equations of motion for linear elasticity with couplestresses are studied. The completeness of a displacement potential similar to theGalerkin-Somigliana representation is proved. The fundamental singular solution of the field equations is defined with the aid of the reciprocal work theorem.
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ON SYSTEMS WITH REGULAR SINGULARITIES, AND THEIR SOLUTIONS [PDF]
Mathematics of the USSR-Izvestiya, 1986 In a space \(C^ n\) an integrable system of differential Pfaff equations of the form \(df=\omega f\) is considered, where f is an unknown p- dimensional vector of complex-valued functions, \(\omega =\sum^{m}_{i=1}A_ i\frac{dL_ i}{L_ i}\) is a matrix differential form, \(A_ i\) are constant commutative complex \(p\times p\)-matrices. It is supposed that
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On the Solution of a Singular Integral Equation [PDF]
Differential Equations, 2003 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Solutions with singularities as almost solutions
Doklady Mathematics, 2006Almost solutions of quasilinear partial differential equations of elliptic type are introduced. The class of equations under consideration contains, in particular, the equations of -harmonic functions, the gas dynamic equation, and some other equations.
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1992
Publisher Summary This chapter elaborates the application and yield of singular solutions. It is applicable to nonlinear ordinary differential equations. It yields a singular solution. Singular solutions may exist where the implicit function theorem does not hold in differential algebraic equations. The algebraic ordinary differential equation F (x,y,
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Publisher Summary This chapter elaborates the application and yield of singular solutions. It is applicable to nonlinear ordinary differential equations. It yields a singular solution. Singular solutions may exist where the implicit function theorem does not hold in differential algebraic equations. The algebraic ordinary differential equation F (x,y,
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Singular solutions for shallow shells
International Journal of Solids and Structures, 1972Abstract Solutions are developed for non-axially symmetric shallow shells subjected to normal surface loading or thermal loading. The singular solutions which correspond to the concentrated normal load, the concentrated application of heat and the concentrated thermal gradient are identified by a consistent limiting process applied to the complete ...
W. Flügge, R.E. Elling
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Singularities in solutions of Burgers' equation
Physics Letters A, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Maurizio Martellini +3 more
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On the solution of optimization problems with singularities
International Journal of Solids and Structures, 1977Abstract We derive a complete set of necessary optimality conditions for a class of variational problems whose extremal solutions are associated with singularities. The use of these conditions is illustrated by two examples involving the optimization of the shapes of elastic bodies with stiffness and stability constraints.
Bhushan Lal Karihaloo, Nikolay Banichuk
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On solutions of a singular diffusion equation
Nonlinear Analysis: Theory, Methods & Applications, 2000Consider the initial-boundary value problem \(u_t=\nabla(a(u)\nabla u)\) in \(\Omega\times(0,T)\), \(\partial u/\partial\nu=g(x,t)\) on \(\partial\Omega\times(0,T)\), \(u(x,0)=u_0(x)\) in \(\Omega\), where \(\Omega\) is a bounded domain in \(\mathbb R^n\), \(g0\) and \(a:(0,\infty)\to\mathbb R\) fulfils \(a>0\), \(a'
Keng Deng, Mingxi Xu
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