Explicit solutions of generalized nonlinear Boussinesq equations.
Explicit Solutions of Nonlocal Boundary Value Problems, Containing Bitsadze-Samarskii Constraints
MSC 2010: 44A35, 35L20, 35J05, 35J25In this paper are found explicit solutions of four nonlocal boundary value problems for Laplace, heat and wave equations, with Bitsadze-Samarskii constraints based on non-classical one-dimensional convolutions. In fact, each explicit solution may be considered as a way for effective summation of a solution in the form of nonharmonic Fourier sine-expansion. Each explicit solution, may be used for numerical calculation of the solutions too.
Explicit solutions of some fractional partial differential equations via stable subordinators.
Exponential-Bessel partial differential equation and Fox’s -function
Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations
In this paper, we study a class of first order nonlinear degenerate partial differential equations with singularity at . Using exponential-type Nagumo norm approach, the Gevrey asymptotic analysis is extended to case of holomorphic parameters in a natural way. A sharp condition is then established to deduce the -summability of the formal solutions. Furthermore, analytical solutions in conical domains are found for each type of these nonlinear singular PDEs.
Extension of formal power series solutions
External ellipsoidal harmonics for the Dunkl-Laplacian.