Partial differential equation

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations

On integrability of the time fractional nonlinear heat conduction equation

Analytical solutions for heat diffusion beyond Fourier law

Generalization of Fourier’s Law into Viscous Heat Equations

Operational Approach and Solutions of Hyperbolic Heat Conduction Equations

Computational analysis of memory-dependent nonlocal response due to ramp-type heating under thermomass thermoelasticity theory

A general numerical method for solving the three-dimensional hyperbolic heat conduction equation on unstructured grids

Derivation of the generalized heat transport equation and comparison with existing models

A generalized coupled biothermoelastic model for human skin based on the Guyer–Krumhansl framework with nonlocal and thermal relaxation effects

Inverse analysis of a loaded heat conduction equation

On a time-optimal control problem for a heat conduction equation with involution