An $$L^{p}$$-Approach to the Well-Posedness of Transport Equations Associated to a Regular Field: Part II
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DOI: 10.1007/s00009-019-1426-7
Abstract: We investigate transport equations associated to a Lipschitz field on some subspace of $\mathbb{R}^N$ endowedwith a general measure $\mu$ in $L^{p}$-spaces $1 < p read more here.
Keywords: equations associated; field; transport; approach well ... See more keywords
Efficient approximation of solutions of parametric linear transport equations by ReLU DNNs
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DOI: 10.1007/s10444-020-09834-7
Abstract: We demonstrate that deep neural networks with the ReLU activation function can efficiently approximate the solutions of various types of parametric linear transport equations. For non-smooth initial conditions, the solutions of these PDEs are high-dimensional… read more here.
Keywords: efficient approximation; parametric linear; transport equations; linear transport ... See more keywords
Inverse source problems in transport equations with external forces
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DOI: 10.1016/j.jde.2021.09.011
Abstract: This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular,… read more here.
Keywords: equations external; source; inverse source; problems transport ... See more keywords
Transition from the Wave Equation to Either the Heat or the Transport Equations through Fractional Differential Expressions
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DOI: 10.3390/sym10100524
Abstract: We present a model that intermediates among the wave, heat, and transport equations. The approach considers the propagation of initial disturbances in a one-dimensional medium that can vibrate. The medium is nonlinear in such a… read more here.
Keywords: differential expressions; heat transport; transport; fractional differential ... See more keywords