Unique Solvability of a Boundary Value Problem for a Loaded Fractional Parabolic-Hyperbolic Equation with Nonlinear Terms
T. K. Yuldashev, O. Kh. Abdullaev
Abstract
This work is devoted to study the existence and uniqueness of solution of an analogue of the Gellerstedt problem with nonlocal assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation with nonlinear terms and Gerasimov–Caputo operator of differentiation. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of successive approximations of factorial law for Volterra type nonlinear integral equations.
Topics & Concepts
MathematicsUniquenessMathematical analysisNonlinear systemBoundary value problemType (biology)Hyperbolic partial differential equationOperator (biology)Work (physics)Hyperbolic functionPartial differential equationTranscription factorBiochemistryPhysicsEcologyChemistryQuantum mechanicsEngineeringRepressorMechanical engineeringBiologyGeneDifferential Equations and Boundary ProblemsDifferential Equations and Numerical MethodsNumerical methods in inverse problems