Abstract: To stabilize partial differential equation (PDE) models, control laws typically require space-dependent functional gains mapped by nonlinear operators from the PDE functional coefficients.
In this article, a solution to a semi-linear PDE is obtained by taking the minimum of solutions to related linear PDEs over an infinite-dimensional space of discount boundaries. By restricting the ...
Tripura, T., & Chakraborty, S. (2023). Wavelet Neural Operator for solving parametric partial differential equations in computational mechanics problems. Computer Methods in Applied Mechanics and ...
In this project, we focus on learning the 1D Allen–Cahn equation using a Fourier neural operator (FNO) model. The Allen–Cahn equation is a reaction-diffusion PDE that describes phase separation in ...
ABSTRACT: This paper is concerned with a modified transitional Korteweg-de Vries equation u t +f( t ) u 2 u x + u xxx =0 , ( x,t )∈ R + × R + with initial value u( x,0 )=g( x )∈ H 4 ( R + ) and ...
Fokker-Planck PDEs (including diffusions) for stable Lévy processes (including Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics, image ...
This is a preview. Log in through your library . Abstract Using a representation in terms of a two-type branching particle system, we prove that positive solutions of the system u̇ = Au+uv, v̇ = Bv+uv ...
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