Combustion Free boundary problem Singular perturbation problems Inhomogeneous problems Monotonicity formula Singular perturbation Variable exponent spaces Viscosity solutions Boundary value problems Classical solution Free-boundary problems Fvee-boundary problem Half derivatives Heat equation High activation energies Inhomogeneous problem Laplace transforms Limit solution Linear and nonlinear stability Lipschitz functions Lipschitz regularity Nonlocal diffusion Nonlocal evolution operator P (x)-Laplacian Quasilinear parabolic operator Regularity Regularity of the free boundary Singular perturbation problem Singular perturbations Two phase