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Differential Operator Equations in Weighted Sobolev Spaces
1999In this chapter we consider the ordinary differential equation with constant operator coefficients $$A({D_t})u = fon\mathbb{R}$$ (2.1) .
Vladimir Kozlov, Vladimir Maz’ya
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Optimal Control for Differential-Operator Equations and Inclusions
2004This chapter deals with optimization problems for evolutional equations of the first order. Let V be a reflective Banach space topologically and densely embedded into the Gilbert space H; \( S = \left[ {0,T} \right],T > 0,L_p \left( {S;V} \right) \) is the space of functions on S with the values in V the Bochner integrated in degree p; $$ X_1 \cap ...
M. Z. Zgurovsky, V. S. Mel’nik
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A class of reaction-diffusion equations with hysteresis differential operator
Applied Mathematics-A Journal of Chinese Universities, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Expansions of Differential Operators and Nonsmooth Solutions of Differential Equations
Cybernetics and Systems Analysis, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Differential operators determining solutions of Elliptic equations
Ukrainian Mathematical Journal, 1995We construct differential operatorsLg(z), Kg(z), Nf¯(z), Mf¯z) which map arbitrary functions holomorphic in a simply connected domainD of the planez=x+iy into regular solutions of the equation $$W_{z\bar z} + A(z,\bar z)W_{\bar z} + B(z,\bar z)W = 0$$ and present examples of the application of these differential operators to the solution of ...
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In-context operator learning with data prompts for differential equation problems
Proceedings of the National Academy of Sciences of the United States of America, 2023Tingwei Meng, Liu Yang, Stanley Osher
exaly
Fractional differential operators and divergence equations
2021Liguang Liu, Jie Xiao
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Distributed and variable order differential-operator equations
2015In Section 5.6 we studied the existence of a solution to the multi-point value problem for a fractional order pseudo-differential equation with m fractional derivatives of the unknown function. This is an example of fractional distributed order differential equations.
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