Spectral bounds for Tricomi problems and application to semilinear existence and existence with uniqueness results

DOI10.1006/jdeq.2001.4139zbMath1157.35436OpenAlexW2058352519MaRDI QIDQ701072

Kevin R. Payne, Daniela Lupo

Publication date: 16 October 2002

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4139

zbMATH Keywords

uniqueness and existencemixed-type operatorTricomi problems

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) PDEs of mixed type (35M10) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

Related Items (15)

A note on the fundamental solution for the Tricomi-type equation in the hyperbolic domain ⋮ On Tricomi problem of Chaplygin's hodograph equation ⋮ On the Strauss index of semilinear Tricomi equation ⋮ The self-similar solutions of the one-dimensional semilinear Tricomi-type equations ⋮ The weighted \(W^{2,p}\) estimate on the solution of the Gellerstedt equation in the upper half space ⋮ Nonexistence for mixed-type equations with critical exponent nonlinearity in a ball ⋮ Global existence for the one-dimensional second order semilinear hyperbolic equations ⋮ Integral Transform Approach to Time-Dependent Partial Differential Equations ⋮ Integral transform approach to generalized Tricomi equations ⋮ On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains ⋮ Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types ⋮ Spectral Theory for Linear Operators of Mixed Type and Applications to Nonlinear Dirichlet Problems ⋮ On the degenerate hyperbolic Goursat problem for linear and nonlinear equations of Tricomi type ⋮ Global Existence for then-Dimensional Semilinear Tricomi-Type Equations ⋮ L²ESTIMATES FOR THE EIGENFUNCTIONS CORRESPONDING TO REAL EIGENVALUES OF THE TRICOMI OPERATOR

Cites Work

• A finite element method for the nonlinear Tricomi problem
• The existence of generalized solutions for a class of quasi-linear equations of mixed type
• A maximum principle for periodic solutions of the telegraph equation
• Combined effects of concave and convex nonlinearities in some elliptic problems
• Existence of eigenvalues for reflected Tricomi operators and applications to multiplicity of solutions for sublinear and asymptotically linear nonlocal Tricomi problems
• A dual variational approach to a class of nonlocal semilinear Tricomi problems
• On the generalized solvability of the Tricomi problem
• ON THE MAXIMUM PRINCIPLE FOR GENERALIZED SOLUTIONS TO THE TRICOMI PROBLEM
• On cauchy's problem for hyperbolic equations and the differentiability of solutions of elliptic equations
• A maximum principle for a class of hyperbolic equations and applications to equations of mixed elliptic-hyperbolic type
• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces
• Weighted sobolev-poincaré inequalities for grushin type operators
• Multiplicity of nontrivial solutions for an asymptotically linear nonlocal Tricomi problem
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