Free boundary problem Combustion 10 Singular perturbation 6 Variable exponent spaces 6 Viscosity solutions 6 Boundary value problems 4 Inhomogeneous problem 4 Regularity 4 Regularity of the free boundary 4 Two phase 4 Classical solution 2 Free-boundary problems 2 Functions 2 Heat equation 2 Heat transfer 2 Laplace transforms 2 Limit solution 2 Lipschitz functions 2 Lipschitz regularity 2 Mathematical models 2 Minimization problem 2 Nonlocal diffusion 2 Nonlocal evolution operator 2 P (x)-Laplacian 2 Problem solving 2 Quasilinear parabolic operator 2 Singular perturbation problem 2 Singular perturbation problems 2 Singular perturbations 2 Uniformly bounded 2