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  1. Calculus of Variations and Partial Differential Equations
  2. Calculus of Variations and Partial Differential Equations : Volume 56
  3. Calculus of Variations and Partial Differential Equations : Volume 56, Issue 2, April 2017
  4. On the global solution problem for semilinear generalized Tricomi equations, I
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Calculus of Variations and Partial Differential Equations : Volume 56
Calculus of Variations and Partial Differential Equations : Volume 56, Issue 3, June 2017
Calculus of Variations and Partial Differential Equations : Volume 56, Issue 2, April 2017
Density of polyhedral partitions
Estimates for the first eigenvalue of Jacobi operator on hypersurfaces with constant mean curvature in spheres
Multiple solutions for a class of semilinear elliptic problems via Nehari-type linking theorem
On minimizers for the isotropic–nematic interface problem
The dual Minkowski problem for negative indices
Monotonicity of solutions for some nonlocal elliptic problems in half-spaces
Global solutions of nonlinear Schrödinger equations
Canceling effects in higher-order Hardy–Sobolev inequalities
Fractional Poincaré inequality with finite total Q-curvature
Maximum principles for a fully nonlinear fractional order equation and symmetry of solutions
Nonhomogeneous Dirichlet problems for the p-Laplacian
On the effect of interactions beyond nearest neighbours on non-convex lattice systems
Minimal graphs in $$Nil_3:$$ existence and non-existence results
Uniaxial versus biaxial character of nematic equilibria in three dimensions
Symmetric Liapunov center theorem
Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains
Remarks on approximate harmonic maps in dimension two
On the global solution problem for semilinear generalized Tricomi equations, I
On the subRiemannian cut locus in a model of free two-step Carnot group
Hölder regularity of quasiminimizers under generalized growth conditions
Semilinear elliptic equations with Hardy potential and subcritical source term
On multi-bump solutions of nonlinear Schrödinger equation with electromagnetic fields and critical nonlinearity in $$\mathbb {R}^N$$
On the p-Laplacian with Robin boundary conditions and boundary trace theorems
Existence of mixed type solutions in the SU(3) Chern–Simons theory in $$\mathbb {R}^2$$
An eigenvalue problem for a fully nonlinear elliptic equation with gradient constraint
Regularity of $$\omega $$ -minimizers for a class of functionals with non-standard growth
Multi-bump solutions for logarithmic Schrödinger equations
Cheeger N-clusters
Global gradient estimates for non-uniformly elliptic equations
Discreteness of interior transmission eigenvalues revisited
Solitary waves for coupled nonlinear elliptic system with nonhomogeneous nonlinearities
Generalized Ginzburg–Landau equations in high dimensions
Analytic aspects of the Tzitzéica equation: blow-up analysis and existence results
Concentration on submanifolds for an Ambrosetti–Prodi type problem
Infinitely many non-radial solutions for fractional Nirenberg problem
Condensation of fermion pairs in a domain
A scalar curvature flow in low dimensions
Isoperimetry with upper mean curvature bounds and sharp stability estimates
Stability of the traveling waves for the derivative Schrödinger equation in the energy space
Calculus of Variations and Partial Differential Equations : Volume 56, Issue 1, February 2017
Calculus of Variations and Partial Differential Equations : Volume 55
Calculus of Variations and Partial Differential Equations : Volume 54
Calculus of Variations and Partial Differential Equations : Volume 53
Calculus of Variations and Partial Differential Equations : Volume 52
Calculus of Variations and Partial Differential Equations : Volume 51
Calculus of Variations and Partial Differential Equations : Volume 50
Calculus of Variations and Partial Differential Equations : Volume 49
Calculus of Variations and Partial Differential Equations : Volume 48
Calculus of Variations and Partial Differential Equations : Volume 47
Calculus of Variations and Partial Differential Equations : Volume 46
Calculus of Variations and Partial Differential Equations : Volume 45
Calculus of Variations and Partial Differential Equations : Volume 44
Calculus of Variations and Partial Differential Equations : Volume 43
Calculus of Variations and Partial Differential Equations : Volume 42
Calculus of Variations and Partial Differential Equations : Volume 41
Calculus of Variations and Partial Differential Equations : Volume 40
Calculus of Variations and Partial Differential Equations : Volume 39
Calculus of Variations and Partial Differential Equations : Volume 38
Calculus of Variations and Partial Differential Equations : Volume 37
Calculus of Variations and Partial Differential Equations : Volume 36
Calculus of Variations and Partial Differential Equations : Volume 35
Calculus of Variations and Partial Differential Equations : Volume 34
Calculus of Variations and Partial Differential Equations : Volume 33
Calculus of Variations and Partial Differential Equations : Volume 32
Calculus of Variations and Partial Differential Equations : Volume 31
Calculus of Variations and Partial Differential Equations : Volume 30
Calculus of Variations and Partial Differential Equations : Volume 29
Calculus of Variations and Partial Differential Equations : Volume 28
Calculus of Variations and Partial Differential Equations : Volume 27
Calculus of Variations and Partial Differential Equations : Volume 26
Calculus of Variations and Partial Differential Equations : Volume 25
Calculus of Variations and Partial Differential Equations : Volume 24
Calculus of Variations and Partial Differential Equations : Volume 23
Calculus of Variations and Partial Differential Equations : Volume 22
Calculus of Variations and Partial Differential Equations : Volume 21
Calculus of Variations and Partial Differential Equations : Volume 20
Calculus of Variations and Partial Differential Equations : Volume 19
Calculus of Variations and Partial Differential Equations : Volume 18
Calculus of Variations and Partial Differential Equations : Volume 17
Calculus of Variations and Partial Differential Equations : Volume 16
Calculus of Variations and Partial Differential Equations : Volume 15
Calculus of Variations and Partial Differential Equations : Volume 14
Calculus of Variations and Partial Differential Equations : Volume 13
Calculus of Variations and Partial Differential Equations : Volume 12
Calculus of Variations and Partial Differential Equations : Volume 11
Calculus of Variations and Partial Differential Equations : Volume 10
Calculus of Variations and Partial Differential Equations : Volume 9
Calculus of Variations and Partial Differential Equations : Volume 8
Calculus of Variations and Partial Differential Equations : Volume 7
Calculus of Variations and Partial Differential Equations : Volume 6
Calculus of Variations and Partial Differential Equations : Volume 5

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On the global solution problem for semilinear generalized Tricomi equations, I

Content Provider SpringerLink
Author Yin, Huicheng He, Daoyin Witt, Ingo
Copyright Year 2017
Abstract In this paper, we are concerned with the global Cauchy problem for the semilinear generalized Tricomi equation $$\partial _t^2 u-t^m \Delta u=|u|^p$$ with initial data $$(u(0,\cdot ), \partial _t u(0,\cdot ))=(u_0, u_1)$$ , where $$t\ge 0$$ , $$x\in \mathbb {R}^n$$ ( $$n\ge 2$$ ), $$m\in \mathbb {N}$$ , $$p>1$$ , and $$u_i\in C_0^{\infty }(\mathbb {R}^n)$$ ( $$i=0,1$$ ). We show that there exists a critical exponent $$p_{\text {crit}}(m,n)>1$$ such that the solution u, in general, blows up in finite time when $$1 p_{\text {crit}}(m,n)$$ such that the solution u exists globally when $$p\ge p_{\text {conf}}(m,n)$$ provided that the initial data is small enough. In case $$p_{\text {crit}}(m,n)
Ending Page 24
Page Count 24
Starting Page 1
File Format PDF
ISSN 09442669
e-ISSN 14320835
Journal Calculus of Variations and Partial Differential Equations
Issue Number 2
Volume Number 56
Language English
Publisher Springer Berlin Heidelberg
Publisher Date 2017-02-09
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Conservation laws Nonlinear second-order hyperbolic equations Systems Theory, Control Calculus of Variations and Optimal Control; Optimization Analysis Theoretical, Mathematical and Computational Physics Shocks and singularities
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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