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A MIXED EQUATION OF TRICOMI–KELDYSH TYPE
Journal of Hyperbolic Differential Equations, 2012We study a mixed type equation, which is analogous, in parts, to Tricomi equation and Keldysh equation. For this equation, the characteristics in the hyperbolic region are transversal to the transition locus in a subset of the locus, but is tangential to it in another subset. We propose a formulation of a closed boundary value problem for such a mixed
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Least-Squares Methods for Mixed-Type Equations
SIAM Journal on Numerical Analysis, 1981A least-squares method for the numerical solution of a class of second-order mixed-type partial differential equations is analyzed. The method offers a unified computational treatment of both elliptic and hyperbolic parts of a given domain. Moreover, it has the advantage over other methods that its implementation is independent of specific properties ...
Sermer, Pavol, Mathon, Rudolf
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Solvability of mixed type operator equations
Applied Mathematics and Computation, 2007This article deals with the following equation \[ x(t)=g(t)+B\bigg(f\bigg(t,\int_0^1u(t,s,Ax(\psi(s)))\,ds\bigg)\bigg) \] (\(A\) and \(B\) are bounded linear operators on \(L_1(0,1)\)) under conditions guaranteeing that the operator \(H\) defined by the right hand side of this equation acts on the space \(L_1(0,1)\).
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Neutral Mixed Type Functional Differential Equations
Journal of Dynamics and Differential Equations, 2015The authors consider implicitly defined equations of mixed type which arose from examining electrical signaling in cardiac tissue and nerve conduction models. They are studying travelling wave solutions \((\phi,c)\) with \(\phi\) waveform and wave speed \(c\) which satisfy the following equation: \[ \sum\limits^N_{j=1}B_j(\xi)\left[-c\phi'(\xi+r_j)+f ...
Lamb, Charles, Van Vleck, Erik S.
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On the numerical solutions of integral equation of mixed type
Journal of Applied Mathematics and Computing, 2003The authors investigate the approximate solutions of mixed Fredholm-Volterra singular integral equation of the second kind with Carleman kernel and logarithmic kernel by using the Toeplitz matrix method and the product Nyström method.
Abdou, M. A. +2 more
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On a Class of Partial Differential Equations of Mixed Type
Journal of Partial Differential Equations, 1988The author considers linear equations of mixed type \[ (1)\quad u_{xx}+yu_{yy}+au_ x+bu_ y+cu=0,\quad c\leq 0, \] where a, b, c are analytic functions of x and y and \(b(x,y)=b_ 0+yb_ 1(x,y)\) \((b_ 0=const)\). Using characteristic coordinates, (1) can be written in the form \[ (2)\quad u_{\xi \eta}-(\beta '/(\xi -\eta))u_{\xi}+(\beta /(\xi -\eta))u_ ...
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On a Problem for a Mixed-Type Equation With Fractional Derivative
Russian Mathematics, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Schrödinger Equation with a Mixed Type Nonlinearity
AIP Conference Proceedings, 2009We study the Cauchy problem for the Schrodinger equation with a mixed type nonlinear term. We analyze the local and global properties of solutions in dependence of the nonlinear power, the repulsive or attractive character of nonlinear interaction and the size of the initial data.
George Venkov +3 more
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On the solution of sets of equations of mixed type
USSR Computational Mathematics and Mathematical Physics, 1970Abstract CERTAIN problems of mathematical physics lead to non-stationary sets of partial differential equations that can be classed neither as parabolic or hyperbolic. This is the case, for instance, when describing the simultaneous propagation of sound and heat in compressible fluid flow [1–3], where the equation of heat conduction is associated ...
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