Cauchy Problems Associated with Certain Integro-Partial Differential Equations [PDF]
Journal of Integral Equations and Applications, 1994 Transmutations and quasi inner products are employed to developed solution representations for a class of initial value problems of the form \[ w_{tt} (x,y,t) = \{I_ x + P(D_ y)\} w(x,y,t), \quad w(x,y,0) = 0, \quad w_ t(x,y,0) = \varphi(x,y). \] Here \(t\) is the time variable and both \(x\) and \(y\) are space variables, \(I_ x\) is an integral ...
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Integro-partial differential equations with singular terminal condition [PDF]
Nonlinear Analysis, 2017 In this paper, we show that the minimal solution of a backward stochastic differential equation gives a probabilistic representation of the minimal viscosity solution of an integro-partial differential equation both with a singular terminal condition.
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A Finite Element Like Scheme for Integro-Partial Differential Hamilton–Jacobi–Bellman Equations [PDF]
SIAM Journal on Numerical Analysis, 2009 We construct a finite element like scheme for fully nonlinear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in finance. The schemes are monotone and robust.
CAMILLI, FABIO, JAKOBSEN E.
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015 We consider the questions of one value solvability of the inverse problem for a nonlinear partial Fredholm type integro-differential equation of the fourth order with degenerate kernel. The method of degenerate kernel is developed for the case of inverse
Tursun K Yuldashev
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Localized direct boundary–domain integro–differential formulations for scalar nonlinear boundary-value problems with variable coefficients [PDF]
, 2005 Mixed boundary-value Problems (BVPs) for a second-order quasi-linear elliptic partial differential equation with variable coefficients dependent on the unknown solution and its gradient are considered.
Mikhailov, SE
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Regularity theory for fully nonlinear integro-differential equations [PDF]
, 2008 We consider nonlinear integro-differential equations, like the ones that arise from stochastic control problems with purely jump L\`evy processes.
Caffarelli, Luis, Silvestre, Luis
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Non-linear degenerate integro-partial differential evolution equations related to geometric Lévy processes and applications to backward stochastic differential equations [PDF]
Stochastics and Stochastic Reports, 2004 We prove a comparison principle for unbounded semicontinuous viscosity sub- and supersolutions of non-linear degenerate parabolic integro-partial differential equations coming from applications in mathematical finance in which geometric Levy processes act as the underlying stochastic processes for the assets dynamics. As a consequence of the “geometric
AMADORI, Anna Lisa +2 more
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Inverse problem for a Fredholm third order partial integro-differential equation
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2014 The solvability of various problems for partial differential equations of the third order is researched in many papers. But, partial Fredholm integro-differential equations of the third order are studied comparatively less. Integro-differential equations
Tursun K Yuldashev
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On the homogenization of partial integro-differential-algebraic equations [PDF]
, 2016 We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics, elasticity, electro ...
Waurick, Marcus
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A new perturbative technique for solving integro-partial differential equations [PDF]
Journal of Mathematical Physics, 1999 Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown distribution function.
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